diff --git a/doc/source/whatsnew/v0.25.0.rst b/doc/source/whatsnew/v0.25.0.rst
index 58c07a14dec39..883dd176f0a59 100644
--- a/doc/source/whatsnew/v0.25.0.rst
+++ b/doc/source/whatsnew/v0.25.0.rst
@@ -312,7 +312,7 @@ Reshaping
 - Bug in :func:`merge` when merging by index name would sometimes result in an incorrectly numbered index (:issue:`24212`)
 - :func:`to_records` now accepts dtypes to its `column_dtypes` parameter (:issue:`24895`)
 - Bug in :func:`concat` where order of ``OrderedDict`` (and ``dict`` in Python 3.6+) is not respected, when passed in as  ``objs`` argument (:issue:`21510`)
-
+- Bug in :func:`concat` where the resulting ``freq`` of two :class:`DatetimeIndex` with the same ``freq`` would be dropped (:issue:`3232`).
 
 Sparse
 ^^^^^^
diff --git a/pandas/core/indexes/datetimelike.py b/pandas/core/indexes/datetimelike.py
index 830f234b85757..da4e7040097a2 100644
--- a/pandas/core/indexes/datetimelike.py
+++ b/pandas/core/indexes/datetimelike.py
@@ -8,6 +8,7 @@
 import numpy as np
 
 from pandas._libs import NaT, iNaT, lib
+from pandas._libs.algos import unique_deltas
 from pandas.compat.numpy import function as nv
 from pandas.errors import AbstractMethodError
 from pandas.util._decorators import Appender, cache_readonly, deprecate_kwarg
@@ -587,11 +588,15 @@ def _concat_same_dtype(self, to_concat, name):
         if len({str(x.dtype) for x in to_concat}) != 1:
             raise ValueError('to_concat must have the same tz')
 
-        if not is_period_dtype(self):
+        new_data = type(self._values)._concat_same_type(to_concat).asi8
+
+        # GH 3232: If the concat result is evenly spaced, we can retain the
+        # original frequency
+        is_diff_evenly_spaced = len(unique_deltas(new_data)) == 1
+        if not is_period_dtype(self) and not is_diff_evenly_spaced:
             # reset freq
             attribs['freq'] = None
 
-        new_data = type(self._values)._concat_same_type(to_concat).asi8
         return self._simple_new(new_data, **attribs)
 
     @Appender(_index_shared_docs['astype'])
diff --git a/pandas/tests/reshape/test_concat.py b/pandas/tests/reshape/test_concat.py
index 08d80a24c092f..bf77ad0b1e7c8 100644
--- a/pandas/tests/reshape/test_concat.py
+++ b/pandas/tests/reshape/test_concat.py
@@ -2532,3 +2532,20 @@ def test_concat_categorical_tz():
         'a', 'b'
     ])
     tm.assert_series_equal(result, expected)
+
+
+def test_concat_datetimeindex_freq():
+    # GH 3232
+    # Monotonic index result
+    dr = pd.date_range('01-Jan-2013', periods=100, freq='50L', tz='UTC')
+    data = list(range(100))
+    expected = pd.DataFrame(data, index=dr)
+    result = pd.concat([expected[:50], expected[50:]])
+    tm.assert_frame_equal(result, expected)
+
+    # Non-monotonic index result
+    result = pd.concat([expected[50:], expected[:50]])
+    expected = pd.DataFrame(data[50:] + data[:50],
+                            index=dr[50:].append(dr[:50]))
+    expected.index.freq = None
+    tm.assert_frame_equal(result, expected)