diff --git a/rest_framework/pagination.py b/rest_framework/pagination.py
index 0255cfc7f..f45db31d6 100644
--- a/rest_framework/pagination.py
+++ b/rest_framework/pagination.py
@@ -572,7 +572,7 @@ class CursorPagination(BasePagination):
         if not self.has_next:
             return None
 
-        if self.cursor and self.cursor.reverse and self.cursor.offset != 0:
+        if self.cursor and self.cursor.reverse and self.cursor.offset != 0 and self.page:
             # If we're reversing direction and we have an offset cursor
             # then we cannot use the first position we find as a marker.
             compare = self._get_position_from_instance(self.page[-1], self.ordering)
@@ -620,7 +620,7 @@ class CursorPagination(BasePagination):
         if not self.has_previous:
             return None
 
-        if self.cursor and not self.cursor.reverse and self.cursor.offset != 0:
+        if self.cursor and not self.cursor.reverse and self.cursor.offset != 0 and self.page:
             # If we're reversing direction and we have an offset cursor
             # then we cannot use the first position we find as a marker.
             compare = self._get_position_from_instance(self.page[0], self.ordering)
diff --git a/tests/test_pagination.py b/tests/test_pagination.py
index dd7f70330..3e8f4b9fa 100644
--- a/tests/test_pagination.py
+++ b/tests/test_pagination.py
@@ -9,7 +9,7 @@ from django.test import TestCase
 from rest_framework import (
     exceptions, filters, generics, pagination, serializers, status
 )
-from rest_framework.pagination import PAGE_BREAK, PageLink
+from rest_framework.pagination import PAGE_BREAK, PageLink, Cursor
 from rest_framework.request import Request
 from rest_framework.test import APIRequestFactory
 
@@ -633,6 +633,16 @@ class CursorPaginationTestsMixin:
 
         assert isinstance(self.pagination.to_html(), type(''))
 
+    def test_offset_cutoff(self):
+        (previous, current, next, previous_url, next_url) = self.get_pages('/')
+
+        next_url = self.pagination.encode_cursor(Cursor(1050, False, None))
+        (previous, current, next, previous_url, next_url) = self.get_pages(next_url)
+
+        assert previous == [7, 7, 7, 8, 9]
+        assert current == []
+        assert next is None
+
 
 class TestCursorPagination(CursorPaginationTestsMixin):
     """