diff --git a/Lib/test/test_ssl.py b/Lib/test/test_ssl.py
index 0aeabc10f2..72b7a94a21 100644
--- a/Lib/test/test_ssl.py
+++ b/Lib/test/test_ssl.py
@@ -2021,6 +2021,16 @@ if _have_threads:
                                 sys.stdout.write(" server: read %r (%s), sending back %r (%s)...\n"
                                                  % (msg, ctype, msg.lower(), ctype))
                             self.write(msg.lower())
+                    except ConnectionResetError:
+                        # XXX: OpenSSL 1.1.1 sometimes raises ConnectionResetError
+                        # when connection is not shut down gracefully.
+                        if self.server.chatty and support.verbose:
+                            sys.stdout.write(
+                                " Connection reset by peer: {}\n".format(
+                                    self.addr)
+                            )
+                        self.close()
+                        self.running = False
                     except OSError:
                         if self.server.chatty:
                             handle_error("Test server failure:\n")