diff --git a/rest_framework/pagination.py b/rest_framework/pagination.py
index a171c684f..762ce58c2 100644
--- a/rest_framework/pagination.py
+++ b/rest_framework/pagination.py
@@ -419,6 +419,8 @@ class LimitOffsetPagination(BasePagination):
             _divide_with_ceil(self.count - self.offset, self.limit) +
             _divide_with_ceil(self.offset, self.limit)
         )
+        if current > final:
+            current = final
 
         def page_number_to_url(page_number):
             if page_number == 1:
diff --git a/tests/test_pagination.py b/tests/test_pagination.py
index 03c4fdf47..63fdbecae 100644
--- a/tests/test_pagination.py
+++ b/tests/test_pagination.py
@@ -435,6 +435,12 @@ class TestLimitOffset:
             ]
         }
 
+    def test_erronous_offset(self):
+        request = Request(factory.get('/', {'limit': 5, 'offset': 1000}))
+        queryset = self.paginate_queryset(request)
+        self.get_paginated_content(queryset)
+        self.get_html_context()
+
     def test_invalid_offset(self):
         """
         An invalid offset query param should be treated as 0.