diff --git a/tornado/websocket.py b/tornado/websocket.py
index d2c6a427aa..edc6993c0c 100644
--- a/tornado/websocket.py
+++ b/tornado/websocket.py
@@ -226,6 +226,8 @@ def __init__(
         self.close_code = None  # type: Optional[int]
         self.close_reason = None  # type: Optional[str]
         self.stream = None  # type: Optional[IOStream]
+        self._opening = False
+        self._need_close = False
         self._on_close_called = False
 
     async def get(self, *args: Any, **kwargs: Any) -> None:
@@ -563,7 +565,9 @@ def on_connection_close(self) -> None:
         if self.ws_connection:
             self.ws_connection.on_connection_close()
             self.ws_connection = None
-        if not self._on_close_called:
+        if self._opening:
+            self._need_close = True
+        elif not self._on_close_called:
             self._on_close_called = True
             self.on_close()
             self._break_cycles()
@@ -950,9 +954,13 @@ async def _accept_connection(self, handler: WebSocketHandler) -> None:
 
         self.start_pinging()
         try:
+            handler._opening = True
             open_result = handler.open(*handler.open_args, **handler.open_kwargs)
             if open_result is not None:
                 await open_result
+            handler._opening = False
+            if handler._need_close:
+                handler.on_connection_close()
         except Exception:
             handler.log_exception(*sys.exc_info())
             self._abort()