diff --git a/doc/source/user_guide/computation.rst b/doc/source/user_guide/computation.rst
index c96e066a5874b..466486586f50b 100644
--- a/doc/source/user_guide/computation.rst
+++ b/doc/source/user_guide/computation.rst
@@ -365,7 +365,8 @@ The list of recognized types are the `scipy.signal window functions
 * ``kaiser`` (needs beta)
 * ``gaussian`` (needs std)
 * ``general_gaussian`` (needs power, width)
-* ``slepian`` (needs width).
+* ``slepian`` (needs width)
+* ``exponential`` (needs tau).
 
 .. ipython:: python
 
diff --git a/doc/source/whatsnew/v0.25.0.rst b/doc/source/whatsnew/v0.25.0.rst
index 3e1ce702f0423..578e24009d35a 100644
--- a/doc/source/whatsnew/v0.25.0.rst
+++ b/doc/source/whatsnew/v0.25.0.rst
@@ -39,6 +39,7 @@ Other Enhancements
 - :class:`datetime.timezone` objects are now supported as arguments to timezone methods and constructors (:issue:`25065`)
 - :meth:`DataFrame.query` and :meth:`DataFrame.eval` now supports quoting column names with backticks to refer to names with spaces (:issue:`6508`)
 - :func:`merge_asof` now gives a more clear error message when merge keys are categoricals that are not equal (:issue:`26136`)
+- :meth:`pandas.core.window.Rolling` supports exponential (or Poisson) window type (:issue:`21303`)
 
 .. _whatsnew_0250.api_breaking:
 
diff --git a/pandas/core/window.py b/pandas/core/window.py
index ffb88b9c4eb65..2d7fdbeffbccc 100644
--- a/pandas/core/window.py
+++ b/pandas/core/window.py
@@ -504,7 +504,8 @@ class Window(_Window):
     * ``kaiser`` (needs beta)
     * ``gaussian`` (needs std)
     * ``general_gaussian`` (needs power, width)
-    * ``slepian`` (needs width).
+    * ``slepian`` (needs width)
+    * ``exponential`` (needs tau), center is set to None.
 
     If ``win_type=None`` all points are evenly weighted. To learn more about
     different window types see `scipy.signal window functions
@@ -623,11 +624,19 @@ def _validate_win_type(win_type, kwargs):
                 arg_map = {'kaiser': ['beta'],
                            'gaussian': ['std'],
                            'general_gaussian': ['power', 'width'],
-                           'slepian': ['width']}
+                           'slepian': ['width'],
+                           'exponential': ['tau'],
+                           }
+
                 if win_type in arg_map:
-                    return tuple([win_type] + _pop_args(win_type,
-                                                        arg_map[win_type],
-                                                        kwargs))
+                    win_args = _pop_args(win_type, arg_map[win_type], kwargs)
+                    if win_type == 'exponential':
+                        # exponential window requires the first arg (center)
+                        # to be set to None (necessary for symmetric window)
+                        win_args.insert(0, None)
+
+                    return tuple([win_type] + win_args)
+
                 return win_type
 
             def _pop_args(win_type, arg_names, kwargs):
diff --git a/pandas/tests/test_window.py b/pandas/tests/test_window.py
index 1d5dd8c2bfcf8..bc6946cbade4c 100644
--- a/pandas/tests/test_window.py
+++ b/pandas/tests/test_window.py
@@ -42,7 +42,8 @@ def win_types(request):
     return request.param
 
 
-@pytest.fixture(params=['kaiser', 'gaussian', 'general_gaussian'])
+@pytest.fixture(params=['kaiser', 'gaussian', 'general_gaussian',
+                        'exponential'])
 def win_types_special(request):
     return request.param
 
@@ -1260,7 +1261,8 @@ def test_cmov_window_special(self, win_types_special):
         kwds = {
             'kaiser': {'beta': 1.},
             'gaussian': {'std': 1.},
-            'general_gaussian': {'power': 2., 'width': 2.}}
+            'general_gaussian': {'power': 2., 'width': 2.},
+            'exponential': {'tau': 10}}
 
         vals = np.array([6.95, 15.21, 4.72, 9.12, 13.81, 13.49, 16.68, 9.48,
                          10.63, 14.48])
@@ -1271,7 +1273,9 @@ def test_cmov_window_special(self, win_types_special):
             'general_gaussian': [np.nan, np.nan, 9.85011, 10.71589, 11.73161,
                                  13.08516, 12.95111, 12.74577, np.nan, np.nan],
             'kaiser': [np.nan, np.nan, 9.86851, 11.02969, 11.65161, 12.75129,
-                       12.90702, 12.83757, np.nan, np.nan]
+                       12.90702, 12.83757, np.nan, np.nan],
+            'exponential': [np.nan, np.nan, 9.83364, 11.10472, 11.64551,
+                            12.66138, 12.92379, 12.83770, np.nan, np.nan],
         }
 
         xp = Series(xps[win_types_special])
@@ -1287,7 +1291,8 @@ def test_cmov_window_special_linear_range(self, win_types_special):
             'kaiser': {'beta': 1.},
             'gaussian': {'std': 1.},
             'general_gaussian': {'power': 2., 'width': 2.},
-            'slepian': {'width': 0.5}}
+            'slepian': {'width': 0.5},
+            'exponential': {'tau': 10}}
 
         vals = np.array(range(10), dtype=np.float)
         xp = vals.copy()