With a variable valve timing mechanisms which changes an open-close timing of an intake valve and/or an exhaust valve in a vehicle engine by using oil pressure to change the rotational phase of a cam shaft with respect to a crank shaft, a delay time is determined in accordance with engine rotational speed, cooling water temperature and the amplitude of a change in the target rotational phase, and fault diagnosis which is performed by comparing the target rotational phase and the actual rotational phase is prohibited for the period of the delay time from after a stepwise change in the target rotation phase.