diff --git a/src/cdk/stepper/stepper.ts b/src/cdk/stepper/stepper.ts
index e7a3f643cba9..9b07794d81a5 100644
--- a/src/cdk/stepper/stepper.ts
+++ b/src/cdk/stepper/stepper.ts
@@ -8,7 +8,7 @@
 
 import {FocusableOption, FocusKeyManager} from '@angular/cdk/a11y';
 import {Direction, Directionality} from '@angular/cdk/bidi';
-import {coerceBooleanProperty} from '@angular/cdk/coercion';
+import {coerceBooleanProperty, coerceNumberProperty} from '@angular/cdk/coercion';
 import {END, ENTER, HOME, SPACE, hasModifierKey} from '@angular/cdk/keycodes';
 import {
   AfterViewInit,
@@ -276,19 +276,21 @@ export class CdkStepper implements AfterViewInit, OnDestroy {
   @Input()
   get selectedIndex() { return this._selectedIndex; }
   set selectedIndex(index: number) {
+    const newIndex = coerceNumberProperty(index);
+
     if (this.steps) {
       // Ensure that the index can't be out of bounds.
-      if (index < 0 || index > this.steps.length - 1) {
+      if (newIndex < 0 || newIndex > this.steps.length - 1) {
         throw Error('cdkStepper: Cannot assign out-of-bounds value to `selectedIndex`.');
       }
 
-      if (this._selectedIndex != index &&
-          !this._anyControlsInvalidOrPending(index) &&
-          (index >= this._selectedIndex || this.steps.toArray()[index].editable)) {
+      if (this._selectedIndex != newIndex &&
+          !this._anyControlsInvalidOrPending(newIndex) &&
+          (newIndex >= this._selectedIndex || this.steps.toArray()[newIndex].editable)) {
         this._updateSelectedItemIndex(index);
       }
     } else {
-      this._selectedIndex = index;
+      this._selectedIndex = newIndex;
     }
   }
   private _selectedIndex = 0;
diff --git a/src/lib/stepper/stepper.spec.ts b/src/lib/stepper/stepper.spec.ts
index 09ba88592217..e25f3f8a1e67 100644
--- a/src/lib/stepper/stepper.spec.ts
+++ b/src/lib/stepper/stepper.spec.ts
@@ -705,13 +705,26 @@ describe('MatStepper', () => {
 
   describe('linear stepper with a pre-defined selectedIndex', () => {
     let preselectedFixture: ComponentFixture<SimplePreselectedMatHorizontalStepperApp>;
+    let stepper: MatHorizontalStepper;
+
     beforeEach(() => {
       preselectedFixture = createComponent(SimplePreselectedMatHorizontalStepperApp);
+      preselectedFixture.detectChanges();
+      stepper = preselectedFixture.debugElement
+          .query(By.directive(MatHorizontalStepper)).componentInstance;
     });
 
     it('should not throw', () => {
       expect(() => preselectedFixture.detectChanges()).not.toThrow();
     });
+
+    it('selectedIndex should be typeof number', () => {
+      expect(typeof stepper.selectedIndex).toBe('number');
+    });
+
+    it('value of selectedIndex should be the pre-defined value', () => {
+      expect(stepper.selectedIndex).toBe(0);
+    });
   });
 
   describe('linear stepper with no `stepControl`', () => {