diff --git a/doc/source/whatsnew/v0.24.0.txt b/doc/source/whatsnew/v0.24.0.txt
index 7ed92935a0991..2bfc57d7f5dcd 100644
--- a/doc/source/whatsnew/v0.24.0.txt
+++ b/doc/source/whatsnew/v0.24.0.txt
@@ -707,6 +707,7 @@ Groupby/Resample/Rolling
 - Multiple bugs in :func:`pandas.core.Rolling.min` with ``closed='left'` and a
   datetime-like index leading to incorrect results and also segfault. (:issue:`21704`)
 - Bug in :meth:`Resampler.apply` when passing postiional arguments to applied func (:issue:`14615`).
+- Bug in :meth:`Series.resample` when passing ``numpy.timedelta64`` to `loffset` kwarg (:issue:`7687`).
 
 Sparse
 ^^^^^^
diff --git a/pandas/core/resample.py b/pandas/core/resample.py
index ae59014ac34f4..2ada4d758d463 100644
--- a/pandas/core/resample.py
+++ b/pandas/core/resample.py
@@ -366,7 +366,8 @@ def _apply_loffset(self, result):
         """
 
         needs_offset = (
-            isinstance(self.loffset, (DateOffset, timedelta)) and
+            isinstance(self.loffset, (DateOffset, timedelta,
+                                      np.timedelta64)) and
             isinstance(result.index, DatetimeIndex) and
             len(result.index) > 0
         )
diff --git a/pandas/tests/test_resample.py b/pandas/tests/test_resample.py
index 38801832829b0..b60fd10d745c1 100644
--- a/pandas/tests/test_resample.py
+++ b/pandas/tests/test_resample.py
@@ -1173,27 +1173,20 @@ def test_resample_frame_basic(self):
         df.resample('M', kind='period').mean()
         df.resample('W-WED', kind='period').mean()
 
-    def test_resample_loffset(self):
+    @pytest.mark.parametrize('loffset', [timedelta(minutes=1),
+                                         '1min', Minute(1),
+                                         np.timedelta64(1, 'm')])
+    def test_resample_loffset(self, loffset):
+        # GH 7687
         rng = date_range('1/1/2000 00:00:00', '1/1/2000 00:13:00', freq='min')
         s = Series(np.random.randn(14), index=rng)
 
         result = s.resample('5min', closed='right', label='right',
-                            loffset=timedelta(minutes=1)).mean()
+                            loffset=loffset).mean()
         idx = date_range('1/1/2000', periods=4, freq='5min')
         expected = Series([s[0], s[1:6].mean(), s[6:11].mean(), s[11:].mean()],
                           index=idx + timedelta(minutes=1))
         assert_series_equal(result, expected)
-
-        expected = s.resample(
-            '5min', closed='right', label='right',
-            loffset='1min').mean()
-        assert_series_equal(result, expected)
-
-        expected = s.resample(
-            '5min', closed='right', label='right',
-            loffset=Minute(1)).mean()
-        assert_series_equal(result, expected)
-
         assert result.index.freq == Minute(5)
 
         # from daily