diff --git a/python/paddle/__init__.py b/python/paddle/__init__.py
index 4e6fe5a686fe1..4b862ab8a0a7f 100755
--- a/python/paddle/__init__.py
+++ b/python/paddle/__init__.py
@@ -246,6 +246,8 @@
 from .tensor.math import angle  # noqa: F401
 from .tensor.math import fmax  # noqa: F401
 from .tensor.math import fmin  # noqa: F401
+from .tensor.math import inner  # noqa: F401
+from .tensor.math import outer  # noqa: F401
 
 from .tensor.random import multinomial  # noqa: F401
 from .tensor.random import standard_normal  # noqa: F401
@@ -495,6 +497,8 @@
            'lgamma',
            'lerp',
            'erfinv',
+           'inner',
+           'outer',
            'square',
            'divide',
            'ceil',
diff --git a/python/paddle/fluid/tests/unittests/test_inner.py b/python/paddle/fluid/tests/unittests/test_inner.py
new file mode 100644
index 0000000000000..de9decd0b8961
--- /dev/null
+++ b/python/paddle/fluid/tests/unittests/test_inner.py
@@ -0,0 +1,166 @@
+# Copyright (c) 2020 PaddlePaddle Authors. All Rights Reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+from __future__ import print_function
+import unittest
+
+import numpy as np
+
+import paddle
+from paddle.static import Program, program_guard
+
+
+class TestMultiplyApi(unittest.TestCase):
+    def _run_static_graph_case(self, x_data, y_data):
+        with program_guard(Program(), Program()):
+            paddle.enable_static()
+            x = paddle.static.data(
+                name='x', shape=x_data.shape, dtype=x_data.dtype)
+            y = paddle.static.data(
+                name='y', shape=y_data.shape, dtype=y_data.dtype)
+            res = paddle.inner(x, y)
+
+            place = paddle.CUDAPlace(0) if paddle.is_compiled_with_cuda(
+            ) else paddle.CPUPlace()
+            exe = paddle.static.Executor(place)
+            outs = exe.run(paddle.static.default_main_program(),
+                           feed={'x': x_data,
+                                 'y': y_data},
+                           fetch_list=[res])
+            res = outs[0]
+            return res
+
+    def _run_dynamic_graph_case(self, x_data, y_data):
+        paddle.disable_static()
+        x = paddle.to_tensor(x_data)
+        y = paddle.to_tensor(y_data)
+        res = paddle.inner(x, y)
+        return res.numpy()
+
+    def test_multiply(self):
+        np.random.seed(7)
+
+        # test static computation graph: 3-d array
+        x_data = np.random.rand(2, 10, 10).astype(np.float64)
+        y_data = np.random.rand(2, 5, 10).astype(np.float64)
+        res = self._run_static_graph_case(x_data, y_data)
+        self.assertTrue(np.allclose(res, np.inner(x_data, y_data)))
+
+        # test static computation graph: 2-d array
+        x_data = np.random.rand(200, 5).astype(np.float64)
+        y_data = np.random.rand(50, 5).astype(np.float64)
+        res = self._run_static_graph_case(x_data, y_data)
+        self.assertTrue(np.allclose(res, np.inner(x_data, y_data)))
+
+        # test static computation graph: 1-d array
+        x_data = np.random.rand(50).astype(np.float64)
+        y_data = np.random.rand(50).astype(np.float64)
+        res = self._run_static_graph_case(x_data, y_data)
+        self.assertTrue(np.allclose(res, np.inner(x_data, y_data)))
+
+        # test dynamic computation graph: 3-d array
+        x_data = np.random.rand(5, 10, 10).astype(np.float64)
+        y_data = np.random.rand(2, 10).astype(np.float64)
+        res = self._run_dynamic_graph_case(x_data, y_data)
+        self.assertTrue(np.allclose(res, np.inner(x_data, y_data)))
+
+        # test dynamic computation graph: 2-d array
+        x_data = np.random.rand(20, 50).astype(np.float64)
+        y_data = np.random.rand(50).astype(np.float64)
+        res = self._run_dynamic_graph_case(x_data, y_data)
+        self.assertTrue(np.allclose(res, np.inner(x_data, y_data)))
+
+        # test dynamic computation graph: Scalar
+        x_data = np.random.rand(20, 10).astype(np.float32)
+        y_data = np.random.rand(1).astype(np.float32).item()
+        res = self._run_dynamic_graph_case(x_data, y_data)
+        self.assertTrue(np.allclose(res, np.inner(x_data, y_data)))
+
+        # test dynamic computation graph: 2-d array Complex
+        x_data = np.random.rand(20,
+                                50).astype(np.float64) + 1J * np.random.rand(
+                                    20, 50).astype(np.float64)
+        y_data = np.random.rand(50).astype(np.float64) + 1J * np.random.rand(
+            50).astype(np.float64)
+        res = self._run_dynamic_graph_case(x_data, y_data)
+        self.assertTrue(np.allclose(res, np.inner(x_data, y_data)))
+
+        # test dynamic computation graph: 3-d array Complex
+        x_data = np.random.rand(5, 10,
+                                10).astype(np.float64) + 1J * np.random.rand(
+                                    5, 10, 10).astype(np.float64)
+        y_data = np.random.rand(2, 10).astype(np.float64) + 1J * np.random.rand(
+            2, 10).astype(np.float64)
+        res = self._run_dynamic_graph_case(x_data, y_data)
+        self.assertTrue(np.allclose(res, np.inner(x_data, y_data)))
+
+
+class TestMultiplyError(unittest.TestCase):
+    def test_errors(self):
+        # test static computation graph: dtype can not be int8
+        paddle.enable_static()
+        with program_guard(Program(), Program()):
+            x = paddle.static.data(name='x', shape=[100], dtype=np.int8)
+            y = paddle.static.data(name='y', shape=[100], dtype=np.int8)
+            self.assertRaises(TypeError, paddle.inner, x, y)
+
+        # test static computation graph: inputs must be broadcastable 
+        with program_guard(Program(), Program()):
+            x = paddle.static.data(name='x', shape=[20, 50], dtype=np.float64)
+            y = paddle.static.data(name='y', shape=[20], dtype=np.float64)
+            self.assertRaises(ValueError, paddle.inner, x, y)
+
+        np.random.seed(7)
+        # test dynamic computation graph: dtype can not be int8
+        paddle.disable_static()
+        x_data = np.random.randn(200).astype(np.int8)
+        y_data = np.random.randn(200).astype(np.int8)
+        x = paddle.to_tensor(x_data)
+        y = paddle.to_tensor(y_data)
+        self.assertRaises(RuntimeError, paddle.inner, x, y)
+
+        # test dynamic computation graph: inputs must be broadcastable
+        x_data = np.random.rand(20, 5)
+        y_data = np.random.rand(10, 2)
+        x = paddle.to_tensor(x_data)
+        y = paddle.to_tensor(y_data)
+        self.assertRaises(ValueError, paddle.inner, x, y)
+
+        # test dynamic computation graph: dtype must be same	
+        x_data = np.random.randn(200).astype(np.float32)
+        y_data = np.random.randn(200).astype(np.float64)
+        x = paddle.to_tensor(x_data)
+        y = paddle.to_tensor(y_data)
+        self.assertRaises(ValueError, paddle.inner, x, y)
+
+        # test dynamic computation graph: dtype must be Tensor type
+        x_data = np.random.randn(200).astype(np.float64)
+        y_data = np.random.randn(200).astype(np.float64)
+        y = paddle.to_tensor(y_data)
+        self.assertRaises(ValueError, paddle.inner, x_data, y)
+
+        # test dynamic computation graph: dtype must be Tensor type
+        x_data = np.random.randn(200).astype(np.float64)
+        y_data = np.random.randn(200).astype(np.float64)
+        x = paddle.to_tensor(x_data)
+        self.assertRaises(ValueError, paddle.inner, x, y_data)
+
+        # test dynamic computation graph: dtype must be Tensor type
+        x_data = np.random.randn(200).astype(np.float32)
+        y_data = np.random.randn(200).astype(np.float32)
+        self.assertRaises(ValueError, paddle.inner, x_data, y_data)
+
+
+if __name__ == '__main__':
+    unittest.main()
diff --git a/python/paddle/fluid/tests/unittests/test_outer.py b/python/paddle/fluid/tests/unittests/test_outer.py
new file mode 100644
index 0000000000000..1b11a71bb2f09
--- /dev/null
+++ b/python/paddle/fluid/tests/unittests/test_outer.py
@@ -0,0 +1,153 @@
+# Copyright (c) 2020 PaddlePaddle Authors. All Rights Reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+from __future__ import print_function
+import unittest
+
+import numpy as np
+
+import paddle
+from paddle.static import Program, program_guard
+
+
+class TestMultiplyApi(unittest.TestCase):
+    def _run_static_graph_case(self, x_data, y_data):
+        with program_guard(Program(), Program()):
+            paddle.enable_static()
+            x = paddle.static.data(
+                name='x', shape=x_data.shape, dtype=x_data.dtype)
+            y = paddle.static.data(
+                name='y', shape=y_data.shape, dtype=y_data.dtype)
+            res = paddle.outer(x, y)
+
+            place = paddle.CUDAPlace(0) if paddle.is_compiled_with_cuda(
+            ) else paddle.CPUPlace()
+            exe = paddle.static.Executor(place)
+            outs = exe.run(paddle.static.default_main_program(),
+                           feed={'x': x_data,
+                                 'y': y_data},
+                           fetch_list=[res])
+            res = outs[0]
+            return res
+
+    def _run_dynamic_graph_case(self, x_data, y_data):
+        paddle.disable_static()
+        x = paddle.to_tensor(x_data)
+        y = paddle.to_tensor(y_data)
+        res = paddle.outer(x, y)
+        return res.numpy()
+
+    def test_multiply(self):
+        np.random.seed(7)
+
+        # test static computation graph: 3-d array
+        x_data = np.random.rand(2, 10, 10).astype(np.float64)
+        y_data = np.random.rand(2, 5, 10).astype(np.float64)
+        res = self._run_static_graph_case(x_data, y_data)
+        self.assertTrue(np.allclose(res, np.outer(x_data, y_data)))
+
+        # test static computation graph: 2-d array
+        x_data = np.random.rand(200, 5).astype(np.float64)
+        y_data = np.random.rand(50, 5).astype(np.float64)
+        res = self._run_static_graph_case(x_data, y_data)
+        self.assertTrue(np.allclose(res, np.outer(x_data, y_data)))
+
+        # test static computation graph: 1-d array
+        x_data = np.random.rand(50).astype(np.float64)
+        y_data = np.random.rand(50).astype(np.float64)
+        res = self._run_static_graph_case(x_data, y_data)
+        self.assertTrue(np.allclose(res, np.outer(x_data, y_data)))
+
+        # test dynamic computation graph: 3-d array
+        x_data = np.random.rand(5, 10, 10).astype(np.float64)
+        y_data = np.random.rand(2, 10).astype(np.float64)
+        res = self._run_dynamic_graph_case(x_data, y_data)
+        self.assertTrue(np.allclose(res, np.outer(x_data, y_data)))
+
+        # test dynamic computation graph: 2-d array
+        x_data = np.random.rand(20, 50).astype(np.float64)
+        y_data = np.random.rand(50).astype(np.float64)
+        res = self._run_dynamic_graph_case(x_data, y_data)
+        self.assertTrue(np.allclose(res, np.outer(x_data, y_data)))
+
+        # test dynamic computation graph: Scalar
+        x_data = np.random.rand(20, 10).astype(np.float32)
+        y_data = np.random.rand(1).astype(np.float32).item()
+        res = self._run_dynamic_graph_case(x_data, y_data)
+        self.assertTrue(np.allclose(res, np.outer(x_data, y_data), rtol=1e4))
+
+        # test dynamic computation graph: 2-d array Complex
+        x_data = np.random.rand(20,
+                                50).astype(np.float64) + 1J * np.random.rand(
+                                    20, 50).astype(np.float64)
+        y_data = np.random.rand(50).astype(np.float64) + 1J * np.random.rand(
+            50).astype(np.float64)
+        res = self._run_dynamic_graph_case(x_data, y_data)
+        self.assertTrue(np.allclose(res, np.outer(x_data, y_data)))
+
+        # test dynamic computation graph: 3-d array Complex
+        x_data = np.random.rand(5, 10,
+                                10).astype(np.float64) + 1J * np.random.rand(
+                                    5, 10, 10).astype(np.float64)
+        y_data = np.random.rand(2, 10).astype(np.float64) + 1J * np.random.rand(
+            2, 10).astype(np.float64)
+        res = self._run_dynamic_graph_case(x_data, y_data)
+        self.assertTrue(np.allclose(res, np.outer(x_data, y_data)))
+
+
+class TestMultiplyError(unittest.TestCase):
+    def test_errors(self):
+        # test static computation graph: dtype can not be int8
+        paddle.enable_static()
+        with program_guard(Program(), Program()):
+            x = paddle.static.data(name='x', shape=[100], dtype=np.int8)
+            y = paddle.static.data(name='y', shape=[100], dtype=np.int8)
+            self.assertRaises(TypeError, paddle.outer, x, y)
+
+        np.random.seed(7)
+        # test dynamic computation graph: dtype can not be int8
+        paddle.disable_static()
+        x_data = np.random.randn(200).astype(np.int8)
+        y_data = np.random.randn(200).astype(np.int8)
+        x = paddle.to_tensor(x_data)
+        y = paddle.to_tensor(y_data)
+        self.assertRaises(RuntimeError, paddle.outer, x, y)
+
+        # test dynamic computation graph: dtype must be same	
+        x_data = np.random.randn(200).astype(np.float32)
+        y_data = np.random.randn(200).astype(np.float64)
+        x = paddle.to_tensor(x_data)
+        y = paddle.to_tensor(y_data)
+        self.assertRaises(ValueError, paddle.outer, x, y)
+
+        # test dynamic computation graph: dtype must be Tensor type
+        x_data = np.random.randn(200).astype(np.float64)
+        y_data = np.random.randn(200).astype(np.float64)
+        y = paddle.to_tensor(y_data)
+        self.assertRaises(ValueError, paddle.outer, x_data, y)
+
+        # test dynamic computation graph: dtype must be Tensor type
+        x_data = np.random.randn(200).astype(np.float32)
+        y_data = np.random.randn(200).astype(np.float32)
+        x = paddle.to_tensor(x_data)
+        self.assertRaises(ValueError, paddle.outer, x, y_data)
+
+        # test dynamic computation graph: dtype must be Tensor type
+        x_data = np.random.randn(200).astype(np.float32)
+        y_data = np.random.randn(200).astype(np.float32)
+        self.assertRaises(ValueError, paddle.outer, x_data, y_data)
+
+
+if __name__ == '__main__':
+    unittest.main()
diff --git a/python/paddle/tensor/__init__.py b/python/paddle/tensor/__init__.py
index ef9425f6db82f..84a62a6ef17fc 100755
--- a/python/paddle/tensor/__init__.py
+++ b/python/paddle/tensor/__init__.py
@@ -213,6 +213,8 @@
 from .math import angle  # noqa: F401
 from .math import fmax  # noqa: F401
 from .math import fmin  # noqa: F401
+from .math import inner  # noqa: F401
+from .math import outer  # noqa: F401
 
 from .random import multinomial  # noqa: F401
 from .random import standard_normal  # noqa: F401
@@ -319,6 +321,8 @@
            'fmax',
            'fmin',
            'mm',
+           'inner',
+           'outer',
            'divide',
            'floor_divide',
            'remainder',
diff --git a/python/paddle/tensor/math.py b/python/paddle/tensor/math.py
index ffe5f580bc624..e878aede13329 100755
--- a/python/paddle/tensor/math.py
+++ b/python/paddle/tensor/math.py
@@ -1195,6 +1195,129 @@ def addmm(input, x, y, beta=1.0, alpha=1.0, name=None):
     return out
 
 
+
+def inner(x, y, name=None):
+    """
+
+    Inner product of two input Tensor.
+    
+    Ordinary inner product for 1-D Tensors, in higher dimensions a sum product over the last axes.
+
+    Args:
+        x (Tensor): An N-D Tensor or a Scalar Tensor. If its not a scalar Tensor, its last dimensions must match y's.
+        y (Tensor): An N-D Tensor or a Scalar Tensor. If its not a scalar Tensor, its last dimensions must match x's.
+        name(str, optional): The default value is None. Normally there is no need for
+            user to set this property. For more information, please refer to :ref:`api_guide_Name`
+
+    Returns:
+        Tensor: The inner-product Tensor, the output shape is x.shape[:-1] + y.shape[:-1].
+
+    Examples:
+        .. code-block:: python
+
+            import paddle
+            x = paddle.arange(1, 7).reshape((2, 3)).astype('float32')
+            y = paddle.arange(1, 10).reshape((3, 3)).astype('float32')
+            out = paddle.inner(x, y)
+            print(out)
+            #        ([[14, 32, 50],
+            #         [32, 77, 122]])
+
+
+    """
+    if x.size == 1 or y.size == 1:
+        return multiply(x, y)
+    else:
+        xshape = x.shape
+        yshape = y.shape
+        dstshape = list(xshape[:-1])+list(yshape[:-1])
+        if len(dstshape)==0:
+            dstshape = [1]
+        nx = x.reshape((-1, xshape[-1]))
+        ny = y.reshape((-1, yshape[-1]))
+
+        if in_dygraph_mode():
+            return _C_ops.matmul_v2(nx, ny.T).reshape(dstshape)
+
+        def __check_input(x, y):
+            var_names = {'x': x, 'y': y}
+            for name, val in var_names.items():
+                check_variable_and_dtype(val, name,
+                                        ['float16', 'float32', 'float64'], 'inner')
+            x_shape = list(xshape)
+            y_shape = list(yshape)
+
+            # check the inner 2 dimensions
+            if x_shape[-1] != y_shape[-1]:
+                if not ((x_shape[-1] == -1) or (y_shape[-1] == -1)):
+                    raise ValueError(
+                        "After performing an optional transpose, Input X's last dim should be "
+                        "equal to Y's last dim for multiplication "
+                        "prerequisites. But received X's shape: %s, Y's shape: %s\n"
+                        % (x_shape, y_shape))
+
+        __check_input(nx, ny)
+
+        helper = LayerHelper('inner', **locals())
+        out = helper.create_variable_for_type_inference(dtype=nx.dtype)
+        helper.append_op(
+            type='matmul_v2', inputs={'X': nx,
+                                'Y': ny.T}, outputs={'Out': out})
+        return out.reshape(dstshape)
+
+
+def outer(x, y, name=None):
+    """
+
+    Outer product of two Tensors.
+
+    Input is flattened if not already 1-dimensional.
+
+    Args:
+        x (Tensor): An N-D Tensor or a Scalar Tensor. 
+        y (Tensor): An N-D Tensor or a Scalar Tensor. 
+        name(str, optional): The default value is None. Normally there is no need for
+            user to set this property. For more information, please refer to :ref:`api_guide_Name`
+
+    Returns:
+        Tensor: The outer-product Tensor.
+
+    Examples:
+        .. code-block:: python
+
+            import paddle
+            x = paddle.arange(1, 4).astype('float32')
+            y = paddle.arange(1, 6).astype('float32')
+            out = paddle.outer(x, y)
+            print(out)
+            #        ([[1, 2, 3, 4, 5],
+            #         [2, 4, 6, 8, 10],
+            #         [3, 6, 9, 12, 15]])
+
+
+    """
+    nx = x.reshape((-1, 1))
+    ny = y.reshape((1, -1))
+
+    if in_dygraph_mode():
+        return _C_ops.matmul_v2(nx, ny)
+
+    def __check_input(x, y):
+        var_names = {'x': x, 'y': y}
+        for name, val in var_names.items():
+            check_variable_and_dtype(val, name,
+                                     ['float16', 'float32', 'float64'], 'inner')
+
+    __check_input(nx, ny)
+
+    helper = LayerHelper('outer', **locals())
+    out = helper.create_variable_for_type_inference(dtype=nx.dtype)
+    helper.append_op(
+        type='matmul_v2', inputs={'X': nx,
+                               'Y': ny}, outputs={'Out': out})
+    return out
+
+
 def logsumexp(x, axis=None, keepdim=False, name=None):
     r"""
     This OP calculates the log of the sum of exponentials of ``x`` along ``axis`` .