diff --git a/doc/source/whatsnew/v0.23.0.txt b/doc/source/whatsnew/v0.23.0.txt
index c6991bc016868..6f5c180c587bd 100644
--- a/doc/source/whatsnew/v0.23.0.txt
+++ b/doc/source/whatsnew/v0.23.0.txt
@@ -525,7 +525,7 @@ Other Enhancements
   library. (:issue:`20564`)
 - Added new writer for exporting Stata dta files in version 117, ``StataWriter117``.  This format supports exporting strings with lengths up to 2,000,000 characters (:issue:`16450`)
 - :func:`to_hdf` and :func:`read_hdf` now accept an ``errors`` keyword argument to control encoding error handling (:issue:`20835`)
-- :func:`date_range` now returns a linearly spaced ``DatetimeIndex`` if ``start``, ``stop``, and ``periods`` are specified, but ``freq`` is not. (:issue:`20808`)
+- :func:`date_range` now returns a linearly spaced ``DatetimeIndex`` if ``start``, ``stop``, and ``periods`` are specified, but ``freq`` is not. (:issue:`20808`, :issue:`20983`)
 
 .. _whatsnew_0230.api_breaking:
 
diff --git a/pandas/core/indexes/datetimes.py b/pandas/core/indexes/datetimes.py
index 1b5aa3b45f3b5..1d5c2d9a098ed 100644
--- a/pandas/core/indexes/datetimes.py
+++ b/pandas/core/indexes/datetimes.py
@@ -587,10 +587,13 @@ def _generate(cls, start, end, periods, name, freq,
                     if end is not None:
                         end = end.tz_localize(tz).asm8
             else:
+                # Create a linearly spaced date_range in local time
+                start = start.tz_localize(tz)
+                end = end.tz_localize(tz)
                 index = tools.to_datetime(np.linspace(start.value,
-                                                      end.value, periods))
-                if tz is not None:
-                    index = index.tz_localize('UTC').tz_convert(tz)
+                                                      end.value, periods),
+                                          utc=True)
+                index = index.tz_convert(tz)
 
         if not left_closed and len(index) and index[0] == start:
             index = index[1:]
diff --git a/pandas/tests/indexes/datetimes/test_date_range.py b/pandas/tests/indexes/datetimes/test_date_range.py
index bbe9cb65eb1a9..3fb088329f225 100644
--- a/pandas/tests/indexes/datetimes/test_date_range.py
+++ b/pandas/tests/indexes/datetimes/test_date_range.py
@@ -164,20 +164,39 @@ def test_date_range_ambiguous_arguments(self):
 
     def test_date_range_convenience_periods(self):
         # GH 20808
-        rng = date_range('2018-04-24', '2018-04-27', periods=3)
-        exp = DatetimeIndex(['2018-04-24 00:00:00', '2018-04-25 12:00:00',
-                             '2018-04-27 00:00:00'], freq=None)
+        result = date_range('2018-04-24', '2018-04-27', periods=3)
+        expected = DatetimeIndex(['2018-04-24 00:00:00',
+                                  '2018-04-25 12:00:00',
+                                  '2018-04-27 00:00:00'], freq=None)
 
-        tm.assert_index_equal(rng, exp)
+        tm.assert_index_equal(result, expected)
 
         # Test if spacing remains linear if tz changes to dst in range
-        rng = date_range('2018-04-01 01:00:00', '2018-04-01 04:00:00',
-                         tz='Australia/Sydney', periods=3)
-        exp = DatetimeIndex(['2018-04-01 01:00:00+11:00',
-                             '2018-04-01 02:00:00+11:00',
-                             '2018-04-01 02:00:00+10:00',
-                             '2018-04-01 03:00:00+10:00',
-                             '2018-04-01 04:00:00+10:00'], freq=None)
+        result = date_range('2018-04-01 01:00:00',
+                            '2018-04-01 04:00:00',
+                            tz='Australia/Sydney',
+                            periods=3)
+        expected = DatetimeIndex([Timestamp('2018-04-01 01:00:00+1100',
+                                            tz='Australia/Sydney'),
+                                  Timestamp('2018-04-01 02:00:00+1000',
+                                            tz='Australia/Sydney'),
+                                  Timestamp('2018-04-01 04:00:00+1000',
+                                            tz='Australia/Sydney')])
+        tm.assert_index_equal(result, expected)
+
+    @pytest.mark.parametrize('start,end,result_tz', [
+        ['20180101', '20180103', 'US/Eastern'],
+        [datetime(2018, 1, 1), datetime(2018, 1, 3), 'US/Eastern'],
+        [Timestamp('20180101'), Timestamp('20180103'), 'US/Eastern'],
+        [Timestamp('20180101', tz='US/Eastern'),
+         Timestamp('20180103', tz='US/Eastern'), 'US/Eastern'],
+        [Timestamp('20180101', tz='US/Eastern'),
+         Timestamp('20180103', tz='US/Eastern'), None]])
+    def test_date_range_linspacing_tz(self, start, end, result_tz):
+        # GH 20983
+        result = date_range(start, end, periods=3, tz=result_tz)
+        expected = date_range('20180101', periods=3, freq='D', tz='US/Eastern')
+        tm.assert_index_equal(result, expected)
 
     def test_date_range_businesshour(self):
         idx = DatetimeIndex(['2014-07-04 09:00', '2014-07-04 10:00',