diff --git a/django/utils/dateparse.py b/django/utils/dateparse.py
index f2c079023f4..cb45a2760b1 100644
--- a/django/utils/dateparse.py
+++ b/django/utils/dateparse.py
@@ -24,7 +24,7 @@ datetime_re = re.compile(
     r'(?P<year>\d{4})-(?P<month>\d{1,2})-(?P<day>\d{1,2})'
     r'[T ](?P<hour>\d{1,2}):(?P<minute>\d{1,2})'
     r'(?::(?P<second>\d{1,2})(?:\.(?P<microsecond>\d{1,6})\d{0,6})?)?'
-    r'(?P<tzinfo>Z|[+-]\d{2}:?\d{2})?$'
+    r'(?P<tzinfo>Z|[+-]\d{2}(?::?\d{2})?)?$'
 )
 
 
@@ -76,7 +76,8 @@ def parse_datetime(value):
         if tzinfo == 'Z':
             tzinfo = utc
         elif tzinfo is not None:
-            offset = 60 * int(tzinfo[1:3]) + int(tzinfo[-2:])
+            offset_mins = int(tzinfo[-2:]) if len(tzinfo) > 3 else 0
+            offset = 60 * int(tzinfo[1:3]) + offset_mins
             if tzinfo[0] == '-':
                 offset = -offset
             tzinfo = get_fixed_timezone(offset)
diff --git a/tests/utils_tests/test_dateparse.py b/tests/utils_tests/test_dateparse.py
index 61afff9a9cf..cdf91c039e0 100644
--- a/tests/utils_tests/test_dateparse.py
+++ b/tests/utils_tests/test_dateparse.py
@@ -39,6 +39,10 @@ class DateParseTests(unittest.TestCase):
             datetime(2012, 4, 9, 4, 8, 16, 0, get_fixed_timezone(-200)))
         self.assertEqual(parse_datetime('2012-04-23T10:20:30.400+02:30'),
             datetime(2012, 4, 23, 10, 20, 30, 400000, get_fixed_timezone(150)))
+        self.assertEqual(parse_datetime('2012-04-23T10:20:30.400+02'),
+            datetime(2012, 4, 23, 10, 20, 30, 400000, get_fixed_timezone(120)))
+        self.assertEqual(parse_datetime('2012-04-23T10:20:30.400-02'),
+            datetime(2012, 4, 23, 10, 20, 30, 400000, get_fixed_timezone(-120)))
         # Invalid inputs
         self.assertEqual(parse_datetime('20120423091500'), None)
         self.assertRaises(ValueError, parse_datetime, '2012-04-56T09:15:90')