diff --git a/doc/source/whatsnew/v0.20.1.txt b/doc/source/whatsnew/v0.20.1.txt
index 504f8004bc8a6e..30b2c71f3b4cff 100644
--- a/doc/source/whatsnew/v0.20.1.txt
+++ b/doc/source/whatsnew/v0.20.1.txt
@@ -18,6 +18,7 @@ Highlights include:
 
 Enhancements
 ~~~~~~~~~~~~
+- ``RangeIndex.append`` now returns a ``RangeIndex`` object when possible (:issue:`16212`)
 
 
 
diff --git a/pandas/core/indexes/range.py b/pandas/core/indexes/range.py
index acd040693af2e9..0b645b46b95b6b 100644
--- a/pandas/core/indexes/range.py
+++ b/pandas/core/indexes/range.py
@@ -443,6 +443,63 @@ def join(self, other, how='left', level=None, return_indexers=False,
         return super(RangeIndex, self).join(other, how, level, return_indexers,
                                             sort)
 
+    def append(self, other):
+        """
+        Append a collection of Index options together
+
+        Parameters
+        ----------
+        other : Index or list/tuple of indices
+
+        Returns
+        -------
+        appended : RangeIndex if all indexes are consecutive RangeIndexes,
+                   otherwise Int64Index or Index
+        """
+
+        to_concat = [self]
+
+        if isinstance(other, (list, tuple)):
+            to_concat = to_concat + list(other)
+        else:
+            to_concat.append(other)
+
+        if not all([isinstance(i, RangeIndex) for i in to_concat]):
+            return super(RangeIndex, self).append(other)
+
+        start = step = next = None
+
+        for obj in to_concat:
+            if not len(obj):
+                continue
+
+            if start is None:
+                # This is set by the first non-empty index
+                start = obj._start
+                if step is None and len(obj) > 1:
+                    step = obj._step
+            elif step is None:
+                # First non-empty index had only one element
+                if obj._start == start:
+                    return super(RangeIndex, self).append(other)
+                step = obj._start - start
+
+            non_consecutive = ((step != obj._step and len(obj) > 1) or
+                               (next is not None and obj._start != next))
+            if non_consecutive:
+                return super(RangeIndex, self).append(other)
+
+            if step is not None:
+                next = obj[-1] + step
+
+        if start is None:
+            start = obj._start
+            step = obj._step
+        stop = obj._stop if next is None else next
+        names = set([obj.name for obj in to_concat])
+        name = None if len(names) > 1 else self.name
+        return RangeIndex(start, stop, step, name=name)
+
     def __len__(self):
         """
         return the length of the RangeIndex
diff --git a/pandas/tests/indexes/test_range.py b/pandas/tests/indexes/test_range.py
index 0379718b004e11..4210962fed51ce 100644
--- a/pandas/tests/indexes/test_range.py
+++ b/pandas/tests/indexes/test_range.py
@@ -941,3 +941,41 @@ def test_where_array_like(self):
         for klass in klasses:
             result = i.where(klass(cond))
             tm.assert_index_equal(result, expected)
+
+    def test_append(self):
+        RI = RangeIndex
+        I64 = Int64Index
+        F64 = Float64Index
+        OI = Index
+        cases = [([RI(1, 12, 5)], RI(1, 12, 5)),
+                 ([RI(0, 6, 4)], RI(0, 6, 4)),
+                 ([RI(1, 3), RI(3, 7)], RI(1, 7)),
+                 ([RI(1, 5, 2), RI(5, 6)], RI(1, 6, 2)),
+                 ([RI(1, 3, 2), RI(4, 7, 3)], RI(1, 7, 3)),
+                 ([RI(-4, 3, 2), RI(4, 7, 2)], RI(-4, 7, 2)),
+                 ([RI(-4, -8), RI(-8, -12)], RI(-8, -12)),
+                 ([RI(-4, -8), RI(3, -4)], RI(3, -8)),
+                 ([RI(-4, -8), RI(3, 5)], RI(3, 5)),
+                 ([RI(-4, -2), RI(3, 5)], I64([-4, -3, 3, 4])),
+                 ([RI(-2,), RI(3, 5)], RI(3, 5)),
+                 ([RI(2,), RI(2)], I64([0, 1, 0, 1])),
+                 ([RI(2,), RI(2, 5), RI(5, 8, 4)], RI(0, 6)),
+                 ([RI(2,), RI(3, 5), RI(5, 8, 4)], I64([0, 1, 3, 4, 5])),
+                 ([RI(-2, 2), RI(2, 5), RI(5, 8, 4)], RI(-2, 6)),
+                 ([RI(3,), pd.Int64Index([-1, 3, 15])],
+                  I64([0, 1, 2, -1, 3, 15])),
+                 ([RI(3,), pd.Float64Index([-1, 3.1, 15.0])],
+                  F64([0, 1, 2, -1, 3.1, 15.0])),
+                 ([RI(3,), pd.Index(['a', None, 14])],
+                  OI([0, 1, 2, 'a', None, 14])),
+                 ([RI(3, 1), pd.Index(['a', None, 14])], OI(['a', None, 14]))
+                 ]
+
+        for indices, expected in cases:
+            result = indices[0].append(indices[1:])
+            tm.assert_index_equal(result, expected, exact=True)
+
+            if len(indices) == 2:
+                # Append single item rather than list
+                result2 = indices[0].append(indices[1])
+                tm.assert_index_equal(result2, expected, exact=True)