diff --git a/lib/redis/index.ts b/lib/redis/index.ts
index 1cf12325..0775c81b 100644
--- a/lib/redis/index.ts
+++ b/lib/redis/index.ts
@@ -304,41 +304,45 @@ Redis.prototype.connect = function (callback) {
           stream.setKeepAlive(true, options.keepAlive);
         }
 
-        stream.once(CONNECT_EVENT, eventHandler.connectHandler(_this));
+        if (stream.connecting) {
+          stream.once(CONNECT_EVENT, eventHandler.connectHandler(_this));
+
+          if (options.connectTimeout) {
+            /*
+             * Typically, Socket#setTimeout(0) will clear the timer
+             * set before. However, in some platforms (Electron 3.x~4.x),
+             * the timer will not be cleared. So we introduce a variable here.
+             *
+             * See https://github.com/electron/electron/issues/14915
+             */
+            let connectTimeoutCleared = false;
+            stream.setTimeout(options.connectTimeout, function () {
+              if (connectTimeoutCleared) {
+                return;
+              }
+              stream.setTimeout(0);
+              stream.destroy();
+
+              const err = new Error("connect ETIMEDOUT");
+              // @ts-ignore
+              err.errorno = "ETIMEDOUT";
+              // @ts-ignore
+              err.code = "ETIMEDOUT";
+              // @ts-ignore
+              err.syscall = "connect";
+              eventHandler.errorHandler(_this)(err);
+            });
+            stream.once(CONNECT_EVENT, function () {
+              connectTimeoutCleared = true;
+              stream.setTimeout(0);
+            });
+          }
+        } else {
+          process.nextTick(eventHandler.connectHandler(_this));
+        }
         stream.once("error", eventHandler.errorHandler(_this));
         stream.once("close", eventHandler.closeHandler(_this));
 
-        if (options.connectTimeout) {
-          /*
-           * Typically, Socket#setTimeout(0) will clear the timer
-           * set before. However, in some platforms (Electron 3.x~4.x),
-           * the timer will not be cleared. So we introduce a variable here.
-           *
-           * See https://github.com/electron/electron/issues/14915
-           */
-          let connectTimeoutCleared = false;
-          stream.setTimeout(options.connectTimeout, function () {
-            if (connectTimeoutCleared) {
-              return;
-            }
-            stream.setTimeout(0);
-            stream.destroy();
-
-            const err = new Error("connect ETIMEDOUT");
-            // @ts-ignore
-            err.errorno = "ETIMEDOUT";
-            // @ts-ignore
-            err.code = "ETIMEDOUT";
-            // @ts-ignore
-            err.syscall = "connect";
-            eventHandler.errorHandler(_this)(err);
-          });
-          stream.once(CONNECT_EVENT, function () {
-            connectTimeoutCleared = true;
-            stream.setTimeout(0);
-          });
-        }
-
         if (options.noDelay) {
           stream.setNoDelay(true);
         }
diff --git a/test/functional/connection.ts b/test/functional/connection.ts
index c8edf79f..78f48893 100644
--- a/test/functional/connection.ts
+++ b/test/functional/connection.ts
@@ -4,6 +4,7 @@ import * as sinon from "sinon";
 import { expect } from "chai";
 import MockServer from "../helpers/mock_server";
 import * as Bluebird from "bluebird";
+import { StandaloneConnector } from "../../lib/connectors";
 
 describe("connection", function () {
   it('should emit "connect" when connected', function (done) {
@@ -423,5 +424,31 @@ describe("connection", function () {
         done();
       });
     });
+
+    it("works when connection established before promise is resolved", (done) => {
+      const socket = new net.Socket();
+      sinon.stub(StandaloneConnector.prototype, "connect").resolves(socket);
+      socket.connect(6379, "127.0.0.1").on("connect", () => {
+        new Redis().on("connect", () => done());
+      });
+    });
+
+    it("ignores connectTimeout when connection established before promise is resolved", (done) => {
+      const socketSetTimeoutSpy = sinon.spy(net.Socket.prototype, "setTimeout");
+      const socket = new net.Socket();
+      sinon.stub(StandaloneConnector.prototype, "connect").resolves(socket);
+      socket.connect(6379, "127.0.0.1").on("connect", () => {
+        const redis = new Redis({
+          connectTimeout: 1,
+        });
+        redis.on("error", () =>
+          done(new Error("Connect timeout should not have been called"))
+        );
+        redis.on("connect", () => {
+          expect(socketSetTimeoutSpy.callCount).to.eql(0);
+          done();
+        });
+      });
+    });
   });
 });