diff --git a/Lib/http/client.py b/Lib/http/client.py
index 745b999942bc99..6828f146a7c353 100644
--- a/Lib/http/client.py
+++ b/Lib/http/client.py
@@ -715,6 +715,9 @@ def _tunnel(self):
             line = response.fp.readline(_MAXLINE + 1)
             if len(line) > _MAXLINE:
                 raise LineTooLong("header line")
+            if not line:
+                # for sites which EOF without sending a trailer
+                break
             if line == b'\r\n':
                 break