diff --git a/Lib/socket.py b/Lib/socket.py
index 5f0a1f40e25..77986fc2e48 100644
--- a/Lib/socket.py
+++ b/Lib/socket.py
@@ -382,7 +382,7 @@ def _sendfile_use_sendfile(self, file, offset=0, count=None):
                     if timeout and not selector_select(timeout):
                         raise TimeoutError('timed out')
                     if count:
-                        blocksize = count - total_sent
+                        blocksize = min(count - total_sent, blocksize)
                         if blocksize <= 0:
                             break
                     try:
diff --git a/Misc/NEWS.d/next/Library/2024-01-15-12-12-54.gh-issue-114077.KcVnfj.rst b/Misc/NEWS.d/next/Library/2024-01-15-12-12-54.gh-issue-114077.KcVnfj.rst
new file mode 100644
index 00000000000..dba086f3a8a
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2024-01-15-12-12-54.gh-issue-114077.KcVnfj.rst
@@ -0,0 +1,2 @@
+Fix possible :exc:`OverflowError` in :meth:`socket.socket.sendfile` when pass
+*count* larger than 2 GiB on 32-bit platform.