diff --git a/rest_framework/fields.py b/rest_framework/fields.py
index 4bea5c419..4eae004dc 100644
--- a/rest_framework/fields.py
+++ b/rest_framework/fields.py
@@ -1329,6 +1329,7 @@ class DurationField(Field):
         'invalid': _('Duration has wrong format. Use one of these formats instead: {format}.'),
         'max_value': _('Ensure this value is less than or equal to {max_value}.'),
         'min_value': _('Ensure this value is greater than or equal to {min_value}.'),
+        'overflow': _('The number of days must be between {min_days} and {max_days}.'),
     }
 
     def __init__(self, **kwargs):
@@ -1347,7 +1348,10 @@ class DurationField(Field):
     def to_internal_value(self, value):
         if isinstance(value, datetime.timedelta):
             return value
-        parsed = parse_duration(str(value))
+        try:
+            parsed = parse_duration(str(value))
+        except OverflowError:
+            self.fail('overflow', min_days=datetime.timedelta.min.days, max_days=datetime.timedelta.max.days)
         if parsed is not None:
             return parsed
         self.fail('invalid', format='[DD] [HH:[MM:]]ss[.uuuuuu]')
diff --git a/tests/test_fields.py b/tests/test_fields.py
index bcdcf15d8..648c2a9c9 100644
--- a/tests/test_fields.py
+++ b/tests/test_fields.py
@@ -1642,10 +1642,14 @@ class TestDurationField(FieldValues):
         '08:01': datetime.timedelta(minutes=8, seconds=1),
         datetime.timedelta(days=3, hours=8, minutes=32, seconds=1, microseconds=123): datetime.timedelta(days=3, hours=8, minutes=32, seconds=1, microseconds=123),
         3600: datetime.timedelta(hours=1),
+        '-999999999 00': datetime.timedelta(days=-999999999),
+        '999999999 00': datetime.timedelta(days=999999999),
     }
     invalid_inputs = {
         'abc': ['Duration has wrong format. Use one of these formats instead: [DD] [HH:[MM:]]ss[.uuuuuu].'],
         '3 08:32 01.123': ['Duration has wrong format. Use one of these formats instead: [DD] [HH:[MM:]]ss[.uuuuuu].'],
+        '-1000000000 00': ['The number of days must be between -999999999 and 999999999.'],
+        '1000000000 00': ['The number of days must be between -999999999 and 999999999.'],
     }
     outputs = {
         datetime.timedelta(days=3, hours=8, minutes=32, seconds=1, microseconds=123): '3 08:32:01.000123',