In valve timing control after issuance of an engine stop instruction with a prescribed value set as a target phase, an ECU delays permission of an engine stop process within a prescribed time period while an intake valve phase has not yet reached the target value, so that a valve timing control operation is continued while the engine operation is continued in an idle state. After the lapse of a prescribed time period from the issuance of the engine stop instruction, however, the ECU permits the engine stop process no matter whether the intake valve phase has reached the target value or not. As a result, the amount of valve timing that can be changed by the valve timing control in the engine stop operation can be increased, without causing any uncomfortable feeling of the driver.