diff --git a/src/cdk/a11y/live-announcer/live-announcer.spec.ts b/src/cdk/a11y/live-announcer/live-announcer.spec.ts
index 84b7c1ceab58..516318cef786 100644
--- a/src/cdk/a11y/live-announcer/live-announcer.spec.ts
+++ b/src/cdk/a11y/live-announcer/live-announcer.spec.ts
@@ -112,6 +112,16 @@ describe('LiveAnnouncer', () => {
       expect(spy).toHaveBeenCalled();
     }));
 
+    it('should resolve the returned promise if another announcement is made before the timeout has expired', fakeAsync(() => {
+      const spy = jasmine.createSpy('announce spy');
+      announcer.announce('something').then(spy);
+      tick(10);
+      announcer.announce('something').then(spy);
+      tick(100);
+
+      expect(spy).toHaveBeenCalledTimes(2);
+    }));
+
     it('should ensure that there is only one live element at a time', fakeAsync(() => {
       fixture.destroy();
 
diff --git a/src/cdk/a11y/live-announcer/live-announcer.ts b/src/cdk/a11y/live-announcer/live-announcer.ts
index cc78425ade11..3f6f5048bd80 100644
--- a/src/cdk/a11y/live-announcer/live-announcer.ts
+++ b/src/cdk/a11y/live-announcer/live-announcer.ts
@@ -31,6 +31,8 @@ export class LiveAnnouncer implements OnDestroy {
   private _liveElement: HTMLElement;
   private _document: Document;
   private _previousTimeout: number;
+  private _currentPromise: Promise<void> | undefined;
+  private _currentResolve: (() => void) | undefined;
 
   constructor(
     @Optional() @Inject(LIVE_ANNOUNCER_ELEMENT_TOKEN) elementToken: any,
@@ -115,17 +117,23 @@ export class LiveAnnouncer implements OnDestroy {
     //   second time without clearing and then using a non-zero delay.
     // (using JAWS 17 at time of this writing).
     return this._ngZone.runOutsideAngular(() => {
-      return new Promise(resolve => {
-        clearTimeout(this._previousTimeout);
-        this._previousTimeout = setTimeout(() => {
-          this._liveElement.textContent = message;
-          resolve();
-
-          if (typeof duration === 'number') {
-            this._previousTimeout = setTimeout(() => this.clear(), duration);
-          }
-        }, 100);
-      });
+      if (!this._currentPromise) {
+        this._currentPromise = new Promise(resolve => (this._currentResolve = resolve));
+      }
+
+      clearTimeout(this._previousTimeout);
+      this._previousTimeout = setTimeout(() => {
+        this._liveElement.textContent = message;
+
+        if (typeof duration === 'number') {
+          this._previousTimeout = setTimeout(() => this.clear(), duration);
+        }
+
+        this._currentResolve!();
+        this._currentPromise = this._currentResolve = undefined;
+      }, 100);
+
+      return this._currentPromise;
     });
   }
 
@@ -144,6 +152,8 @@ export class LiveAnnouncer implements OnDestroy {
     clearTimeout(this._previousTimeout);
     this._liveElement?.remove();
     this._liveElement = null!;
+    this._currentResolve?.();
+    this._currentPromise = this._currentResolve = undefined;
   }
 
   private _createLiveElement(): HTMLElement {