diff --git a/doc/source/whatsnew/v0.16.1.txt b/doc/source/whatsnew/v0.16.1.txt
index 493f299b2bf32..e0ee88f6eb10c 100755
--- a/doc/source/whatsnew/v0.16.1.txt
+++ b/doc/source/whatsnew/v0.16.1.txt
@@ -320,3 +320,4 @@ Bug Fixes
 - Google BigQuery connector now imports dependencies on a per-method basis.(:issue:`9713`)
 - Updated BigQuery connector to no longer use deprecated ``oauth2client.tools.run()`` (:issue:`8327`)
 - Bug in subclassed ``DataFrame``. It may not return the correct class, when slicing or subsetting it. (:issue:`9632`)
+- BUG in median() where non-float null values are not handled correctly (:issue:`10040`)
diff --git a/pandas/core/nanops.py b/pandas/core/nanops.py
index f68f4f9037d97..4121dd8e89bee 100644
--- a/pandas/core/nanops.py
+++ b/pandas/core/nanops.py
@@ -285,6 +285,7 @@ def get_median(x):
 
     if values.dtype != np.float64:
         values = values.astype('f8')
+        values[mask] = np.nan
 
     if axis is None:
         values = values.ravel()
diff --git a/pandas/tseries/tests/test_timedeltas.py b/pandas/tseries/tests/test_timedeltas.py
index faf4e3fa57780..45145eb7ab7e8 100644
--- a/pandas/tseries/tests/test_timedeltas.py
+++ b/pandas/tseries/tests/test_timedeltas.py
@@ -614,7 +614,7 @@ def test_timedelta_ops(self):
         self.assertEqual(result, expected)
 
         result = td.median()
-        expected = to_timedelta('00:00:08')
+        expected = to_timedelta('00:00:09')
         self.assertEqual(result, expected)
 
         result = td.to_frame().median()
@@ -641,6 +641,14 @@ def test_timedelta_ops(self):
         for op in ['skew','kurt','sem','var','prod']:
             self.assertRaises(TypeError, lambda : getattr(td,op)())
 
+        # GH 10040
+        # make sure NaT is properly handled by median()
+        s = Series([Timestamp('2015-02-03'), Timestamp('2015-02-07')])
+        self.assertEqual(s.diff().median(), timedelta(days=4))
+
+        s = Series([Timestamp('2015-02-03'), Timestamp('2015-02-07'), Timestamp('2015-02-15')])
+        self.assertEqual(s.diff().median(), timedelta(days=6))
+
     def test_timedelta_ops_scalar(self):
         # GH 6808
         base = pd.to_datetime('20130101 09:01:12.123456')