diff --git a/spec/observables/dom/webSocket-spec.ts b/spec/observables/dom/webSocket-spec.ts
index 854e9369da..6a3e0b6f9c 100644
--- a/spec/observables/dom/webSocket-spec.ts
+++ b/spec/observables/dom/webSocket-spec.ts
@@ -171,6 +171,32 @@ describe('webSocket', () => {
       (<any>socket.close).restore();
     });
 
+    it('should close the socket when unsubscribed while connecting', () => {
+      const subject = webSocket<string>('ws://mysocket');
+      subject.subscribe();
+      const socket = MockWebSocket.lastSocket;
+      sinon.spy(socket, 'close');
+      subject.unsubscribe();
+
+      expect(socket.close).have.been.called;
+      expect(socket.readyState).to.equal(3); // closed
+
+      (<any>socket.close).restore();
+    });
+
+    it('should close the socket when subscription is cancelled while connecting', () => {
+      const subject = webSocket<string>('ws://mysocket');
+      const subscription = subject.subscribe();
+      const socket = MockWebSocket.lastSocket;
+      sinon.spy(socket, 'close');
+      subscription.unsubscribe();
+
+      expect(socket.close).have.been.called;
+      expect(socket.readyState).to.equal(3); // closed
+
+      (<any>socket.close).restore();
+    });
+
     it('should close the socket with a code and a reason when errored', () => {
       const subject = webSocket<string>('ws://mysocket');
       subject.subscribe();
diff --git a/src/internal/observable/dom/WebSocketSubject.ts b/src/internal/observable/dom/WebSocketSubject.ts
index 0700382222..c6e4f2e6dd 100644
--- a/src/internal/observable/dom/WebSocketSubject.ts
+++ b/src/internal/observable/dom/WebSocketSubject.ts
@@ -367,7 +367,7 @@ export class WebSocketSubject<T> extends AnonymousSubject<T> {
     subscriber.add(() => {
       const { _socket } = this;
       if (this._output.observers.length === 0) {
-        if (_socket && _socket.readyState === 1) {
+        if (_socket && (_socket.readyState === 1 || _socket.readyState === 0)) {
           _socket.close();
         }
         this._resetState();
@@ -378,7 +378,7 @@ export class WebSocketSubject<T> extends AnonymousSubject<T> {
 
   unsubscribe() {
     const { _socket } = this;
-    if (_socket && _socket.readyState === 1) {
+    if (_socket && (_socket.readyState === 1 || _socket.readyState === 0)) {
       _socket.close();
     }
     this._resetState();