diff --git a/uvicorn/protocols/websockets/websockets_sansio_impl.py b/uvicorn/protocols/websockets/websockets_sansio_impl.py
index 880982afa..e8fd063a1 100644
--- a/uvicorn/protocols/websockets/websockets_sansio_impl.py
+++ b/uvicorn/protocols/websockets/websockets_sansio_impl.py
@@ -369,7 +369,8 @@ async def send(self, message: ASGISendEvent) -> None:
                     elif text_data is not None:
                         self.conn.send_text(text_data.encode())
                     output = self.conn.data_to_send()
-                    self.transport.write(b"".join(output))
+                    if not self.transport.is_closing():
+                        self.transport.write(b"".join(output))
 
                 elif message_type == "websocket.close":
                     if not self.transport.is_closing():