diff --git a/doc/source/whatsnew/v0.20.0.txt b/doc/source/whatsnew/v0.20.0.txt
index 9ea7b740bae8f..3463351d8e349 100644
--- a/doc/source/whatsnew/v0.20.0.txt
+++ b/doc/source/whatsnew/v0.20.0.txt
@@ -366,3 +366,5 @@ Bug Fixes
 
 
 - Bug in ``pd.read_csv()`` for the C engine where ``usecols`` were being indexed incorrectly with ``parse_dates`` (:issue:`14792`)
+
+- Bug in ``Series.dt.round`` inconsistent behaviour on NAT's with different arguments (:issue:`14940`)
\ No newline at end of file
diff --git a/pandas/tseries/base.py b/pandas/tseries/base.py
index 63e56e09e91fe..a8dd2238c2063 100644
--- a/pandas/tseries/base.py
+++ b/pandas/tseries/base.py
@@ -84,6 +84,7 @@ def _round(self, freq, rounder):
         values = _ensure_datetimelike_to_i8(self)
 
         result = (unit * rounder(values / float(unit))).astype('i8')
+        result = self._maybe_mask_results(result, fill_value=tslib.NaT)
         attribs = self._get_attributes_dict()
         if 'freq' in attribs:
             attribs['freq'] = None
diff --git a/pandas/tseries/tests/test_timeseries.py b/pandas/tseries/tests/test_timeseries.py
index b7e77c2eb770a..1d622cbd46997 100644
--- a/pandas/tseries/tests/test_timeseries.py
+++ b/pandas/tseries/tests/test_timeseries.py
@@ -4441,6 +4441,15 @@ def test_nat_operations(self):
         self.assertEqual(s.min(), exp)
         self.assertEqual(s.max(), exp)
 
+    def test_round_nat(self):
+        # GH14940
+        s = Series([pd.NaT])
+        expected = Series(pd.NaT)
+        for method in ["round", "floor", "ceil"]:
+            round_method = getattr(s.dt, method)
+            for freq in ["s", "5s", "min", "5min", "h", "5h"]:
+                assert_series_equal(round_method(freq), expected)
+
 
 class TestTimestamp(tm.TestCase):
     def test_class_ops_pytz(self):
@@ -4849,6 +4858,15 @@ def test_is_leap_year(self):
         self.assertFalse(pd.NaT.is_leap_year)
         self.assertIsInstance(pd.NaT.is_leap_year, bool)
 
+    def test_round_nat(self):
+        # GH14940
+        ts = Timestamp('nat')
+        print(dir(ts))
+        for method in ["round", "floor", "ceil"]:
+            round_method = getattr(ts, method)
+            for freq in ["s", "5s", "min", "5min", "h", "5h"]:
+                self.assertIs(round_method(freq), ts)
+
 
 class TestSlicing(tm.TestCase):
     def test_slice_year(self):
diff --git a/pandas/tslib.pyx b/pandas/tslib.pyx
index 9a20c36638bce..215e15d60837a 100644
--- a/pandas/tslib.pyx
+++ b/pandas/tslib.pyx
@@ -885,7 +885,12 @@ def _make_nan_func(func_name):
     f.__name__ = func_name
     return f
 
+
+# GH14940
+_round_methods = ['round', 'floor', 'ceil']
+
 _nat_methods = ['date', 'now', 'replace', 'to_pydatetime', 'today']
+_nat_methods.extend(_round_methods)
 
 _nan_methods = ['weekday', 'isoweekday', 'total_seconds']
 
@@ -895,7 +900,7 @@ _implemented_methods.extend(_nan_methods)
 
 for _method_name in _nat_methods:
     # not all methods exist in all versions of Python
-    if hasattr(NaTType, _method_name):
+    if hasattr(NaTType, _method_name) or _method_name in _round_methods:
         setattr(NaTType, _method_name, _make_nat_func(_method_name))
 
 for _method_name in _nan_methods: