diff --git a/doc/source/whatsnew/v0.20.0.txt b/doc/source/whatsnew/v0.20.0.txt
index d89103309e990..f534c67273560 100644
--- a/doc/source/whatsnew/v0.20.0.txt
+++ b/doc/source/whatsnew/v0.20.0.txt
@@ -59,6 +59,7 @@ Other enhancements
 - ``Series`` provides a ``to_excel`` method to output Excel files (:issue:`8825`)
 - The ``usecols`` argument in ``pd.read_csv`` now accepts a callable function as a value  (:issue:`14154`)
 - ``pd.DataFrame.plot`` now prints a title above each subplot if ``suplots=True`` and ``title`` is a list of strings (:issue:`14753`)
+- ``pd.Series.interpolate`` now supports timedelta as an index type with ``method='time'`` (:issue:`6424`)
 
 .. _whatsnew_0200.api_breaking:
 
diff --git a/pandas/core/missing.py b/pandas/core/missing.py
index b847415f274db..f1191ff1c7009 100644
--- a/pandas/core/missing.py
+++ b/pandas/core/missing.py
@@ -12,7 +12,8 @@
                                  is_float_dtype, is_datetime64_dtype,
                                  is_integer_dtype, _ensure_float64,
                                  is_scalar,
-                                 _DATELIKE_DTYPES)
+                                 _DATELIKE_DTYPES,
+                                 needs_i8_conversion)
 from pandas.types.missing import isnull
 
 
@@ -187,7 +188,7 @@ def _interp_limit(invalid, fw_limit, bw_limit):
         if method in ('values', 'index'):
             inds = np.asarray(xvalues)
             # hack for DatetimeIndex, #1646
-            if issubclass(inds.dtype.type, np.datetime64):
+            if needs_i8_conversion(inds.dtype.type):
                 inds = inds.view(np.int64)
             if inds.dtype == np.object_:
                 inds = lib.maybe_convert_objects(inds)
diff --git a/pandas/tests/series/test_missing.py b/pandas/tests/series/test_missing.py
index 4e6c58df54dfd..5666a07cad4b8 100644
--- a/pandas/tests/series/test_missing.py
+++ b/pandas/tests/series/test_missing.py
@@ -891,6 +891,23 @@ def test_spline_error(self):
         with tm.assertRaises(ValueError):
             s.interpolate(method='spline', order=0)
 
+    def test_interp_timedelta64(self):
+        # GH 6424
+        df = Series([1, np.nan, 3],
+                    index=pd.to_timedelta([1, 2, 3]))
+        result = df.interpolate(method='time')
+        expected = Series([1., 2., 3.],
+                          index=pd.to_timedelta([1, 2, 3]))
+        assert_series_equal(result, expected)
+
+        # test for non uniform spacing
+        df = Series([1, np.nan, 3],
+                    index=pd.to_timedelta([1, 2, 4]))
+        result = df.interpolate(method='time')
+        expected = Series([1., 1.666667, 3.],
+                          index=pd.to_timedelta([1, 2, 4]))
+        assert_series_equal(result, expected)
+
 
 if __name__ == '__main__':
     import nose