In a control device, an engine self-restart means tries the engine restart when an engine restart request is issued while the engine rotation speed is within a first rotation speed range. A pre-gear synchronizing control means executes gear rotation speed synchronization between pinion and ring gears, and then retries the engine restart when the engine restart request is issued while the engine rotation-speed is within a second rotation speed range. A pre-gear meshing control means executes gear-meshing between the pinion and ring gears and then retries the engine restart when the engine restart request is issued while the engine rotation speed is within a third rotation speed range. On detecting the engine-restart failure of the engine self-restart control, the control device prohibits the execution of pre-gear synchronizing control until a predetermined time counted form the failure detection time is elapsed, and executes the pre-gear meshing control after the predetermined time period is elapsed.