diff --git a/lib/winston/transports/file.js b/lib/winston/transports/file.js
index 60af7f580..b38584bc2 100644
--- a/lib/winston/transports/file.js
+++ b/lib/winston/transports/file.js
@@ -88,6 +88,7 @@ module.exports = class File extends TransportStream {
     this._drain = false;
     this._opening = false;
     this._ending = false;
+    this._writeStreams = [];
 
     if (this.dirname) this._createLogDirIfNotExist(this.dirname);
     this.open();
@@ -400,6 +401,9 @@ module.exports = class File extends TransportStream {
       debug('stat done: %s { size: %s }', this.filename, size);
       this._size = size;
       this._dest = this._createStream(this._stream);
+
+      this._writeStreams.push(this._dest);
+
       this._opening = false;
       this.once('open', () => {
         if (this._stream.eventNames().includes('rotate')) {
@@ -503,6 +507,12 @@ module.exports = class File extends TransportStream {
   _cleanupStream(stream) {
     stream.removeListener('error', this._onError);
 
+    let streamToClose = this._writeStreams.pop();
+    while (streamToClose) {
+      streamToClose.destroy();
+      streamToClose = this._writeStreams.pop();
+    }
+
     return stream;
   }