After a delay control for extending a period from when an engine stop request is made to when the engine actually stops is started, the electronic control unit changes the valve timing and the valve duration of an intake valve to valve timing and valve duration suitable for starting the engine. When changing the valve timing and the valve duration after the start of the delay control, the electronic control unit changes one of the valve timing and the valve duration of the intake valve based on the other such a valve overlap becomes less than or equal to a predetermined value.