diff --git a/src/material/tabs/tab-group.spec.ts b/src/material/tabs/tab-group.spec.ts
index e4cb95cd4667..11a25a038aee 100644
--- a/src/material/tabs/tab-group.spec.ts
+++ b/src/material/tabs/tab-group.spec.ts
@@ -6,7 +6,14 @@ import {By} from '@angular/platform-browser';
 import {BrowserAnimationsModule, NoopAnimationsModule} from '@angular/platform-browser/animations';
 import {CommonModule} from '@angular/common';
 import {Observable} from 'rxjs';
-import {MatTab, MatTabGroup, MatTabHeaderPosition, MatTabsModule, MAT_TABS_CONFIG} from './index';
+import {
+  MatTab,
+  MatTabGroup,
+  MatTabHeader,
+  MatTabHeaderPosition,
+  MatTabsModule,
+  MAT_TABS_CONFIG
+} from './index';
 
 
 describe('MatTabGroup', () => {
@@ -298,6 +305,22 @@ describe('MatTabGroup', () => {
       expect(tabLabelNativeElements.every(el => el.classList.contains('mat-focus-indicator')))
         .toBe(true);
     });
+
+    it('should be able to programmatically focus a particular tab', () => {
+      fixture.detectChanges();
+      const tabGroup: MatTabGroup =
+          fixture.debugElement.query(By.css('mat-tab-group')).componentInstance;
+      const tabHeader: MatTabHeader =
+          fixture.debugElement.query(By.css('mat-tab-header')).componentInstance;
+
+      expect(tabHeader.focusIndex).not.toBe(3);
+
+      tabGroup.focusTab(3);
+      fixture.detectChanges();
+
+      expect(tabHeader.focusIndex).not.toBe(3);
+    });
+
   });
 
   describe('aria labelling', () => {
diff --git a/src/material/tabs/tab-group.ts b/src/material/tabs/tab-group.ts
index 500bd997d73a..f3c41110fbd7 100644
--- a/src/material/tabs/tab-group.ts
+++ b/src/material/tabs/tab-group.ts
@@ -286,6 +286,18 @@ export abstract class _MatTabGroupBase extends _MatTabGroupMixinBase implements
     }
   }
 
+  /**
+   * Sets focus to a particular tab.
+   * @param index Index of the tab to be focused.
+   */
+  focusTab(index: number) {
+    const header = this._tabHeader;
+
+    if (header) {
+      header.focusIndex = index;
+    }
+  }
+
   _focusChanged(index: number) {
     this.focusChange.emit(this._createChangeEvent(index));
   }
diff --git a/tools/public_api_guard/material/tabs.d.ts b/tools/public_api_guard/material/tabs.d.ts
index 262add0b7b99..88a7ca735b54 100644
--- a/tools/public_api_guard/material/tabs.d.ts
+++ b/tools/public_api_guard/material/tabs.d.ts
@@ -58,6 +58,7 @@ export declare abstract class _MatTabGroupBase extends _MatTabGroupMixinBase imp
     _handleClick(tab: MatTab, tabHeader: MatTabGroupBaseHeader, index: number): void;
     _removeTabBodyWrapperHeight(): void;
     _setTabBodyWrapperHeight(tabHeight: number): void;
+    focusTab(index: number): void;
     ngAfterContentChecked(): void;
     ngAfterContentInit(): void;
     ngOnDestroy(): void;