diff --git a/doc/source/whatsnew/v0.17.0.txt b/doc/source/whatsnew/v0.17.0.txt
index 31b6bb0d5575d..4acd77222efd7 100644
--- a/doc/source/whatsnew/v0.17.0.txt
+++ b/doc/source/whatsnew/v0.17.0.txt
@@ -865,4 +865,5 @@ Bug Fixes
 - Bug in ``to_json`` which was causing segmentation fault when serializing 0-rank ndarray (:issue:`9576`)
 - Bug in plotting functions may raise ``IndexError`` when plotted on ``GridSpec`` (:issue:`10819`)
 - Bug in plot result may show unnecessary minor ticklabels (:issue:`10657`)
-- Bug when constructing ``DataFrame`` where passing a dictionary with only scalar values and specifying columns did not raise an error (:issue:`10856`)
+- Bug in ``groupby`` incorrect computation for aggregation on ``DataFrame`` with ``NaT`` (E.g ``first``, ``last``, ``min``). (:issue:`10590`)
+- Bug when constructing ``DataFrame`` where passing a dictionary with only scalar values and specifying columns did not raise an error (:issue:`10856`)
\ No newline at end of file
diff --git a/pandas/core/groupby.py b/pandas/core/groupby.py
index 534117b8e9249..1a40b73de8dd2 100644
--- a/pandas/core/groupby.py
+++ b/pandas/core/groupby.py
@@ -1532,6 +1532,7 @@ def aggregate(self, values, how, axis=0):
 
         if is_datetime_or_timedelta_dtype(values.dtype):
             values = values.view('int64')
+            values[values == tslib.iNaT] = np.nan
             # GH 7754
             is_numeric = True
         elif is_bool_dtype(values.dtype):
@@ -2761,9 +2762,7 @@ def _cython_agg_blocks(self, how, numeric_only=True):
 
         for block in data.blocks:
 
-            values = block._try_operate(block.values)
-
-            result, _ = self.grouper.aggregate(values, how, axis=agg_axis)
+            result, _ = self.grouper.aggregate(block.values, how, axis=agg_axis)
 
             # see if we can cast the block back to the original dtype
             result = block._try_coerce_and_cast_result(result)
diff --git a/pandas/tests/test_groupby.py b/pandas/tests/test_groupby.py
index 41703b3b5a3b7..ec6ab4e0d2ab1 100644
--- a/pandas/tests/test_groupby.py
+++ b/pandas/tests/test_groupby.py
@@ -5413,6 +5413,24 @@ def test_func(x):
         expected = DataFrame()
         tm.assert_frame_equal(result, expected)
 
+    def test_first_last_max_min_on_time_data(self):
+        # GH 10295
+        # Verify that NaT is not in the result of max, min, first and last on
+        # Dataframe with datetime or timedelta values.
+        from datetime import timedelta as td
+        df_test=DataFrame({'dt':[nan,'2015-07-24 10:10','2015-07-25 11:11','2015-07-23 12:12',nan],
+                           'td':[nan,td(days=1),td(days=2),td(days=3),nan]})
+        df_test.dt=pd.to_datetime(df_test.dt)
+        df_test['group']='A'
+        df_ref=df_test[df_test.dt.notnull()]
+
+        grouped_test=df_test.groupby('group')
+        grouped_ref=df_ref.groupby('group')
+
+        assert_frame_equal(grouped_ref.max(),grouped_test.max())
+        assert_frame_equal(grouped_ref.min(),grouped_test.min())
+        assert_frame_equal(grouped_ref.first(),grouped_test.first())
+        assert_frame_equal(grouped_ref.last(),grouped_test.last())
 
 def assert_fp_equal(a, b):
     assert (np.abs(a - b) < 1e-12).all()