diff --git a/pandas/core/resample.py b/pandas/core/resample.py
index 2308f9edb4328..a234bf9800844 100644
--- a/pandas/core/resample.py
+++ b/pandas/core/resample.py
@@ -86,6 +86,8 @@
     Tick,
 )
 
+from pandas.core.reshape.concat import concat
+
 _shared_docs_kwargs: Dict[str, str] = {}
 
 
@@ -859,6 +861,11 @@ def interpolate(
         Interpolate values according to different methods.
         """
         result = self._upsample("asfreq")
+        if isinstance(result.index, DatetimeIndex):
+            obj = self._selected_obj
+            tmp = concat([obj, result]).sort_index().interpolate(method='time')
+            tmp = tmp[result.index]
+            result[...] = tmp[~tmp.index.duplicated(keep='first')]
         return result.interpolate(
             method=method,
             axis=axis,
diff --git a/pandas/tests/resample/test_datetime_index.py b/pandas/tests/resample/test_datetime_index.py
index cbf69696d5801..0b4a9bd10e0bf 100644
--- a/pandas/tests/resample/test_datetime_index.py
+++ b/pandas/tests/resample/test_datetime_index.py
@@ -1816,3 +1816,14 @@ def test_resample_aggregate_functions_min_count(func):
         index=DatetimeIndex(["2020-03-31"], dtype="datetime64[ns]", freq="Q-DEC"),
     )
     tm.assert_series_equal(result, expected)
+
+
+def timeseries_interpolation():
+    dates1 = date_range('2016-08-28', periods=4, freq='21H')
+    ts1 = Series([21 * i for i in range(4)], dates1, dtype=float)
+    nb_periods = (21 * 4) // 15
+    dates2 = date_range('2016-08-28', periods=nb_periods, freq='15H')
+    expect = Series([15 * i for i in range(nb_periods)], dates2, dtype=float)
+
+    result = ts1.resample('15H').interpolate(method='time')
+    tm.assert_series_equal(result, expect)