On a vehicle equipped with a vacuum-assist type of brake booster utilizing the intake air pressure of the vehicle engine, an engine control apparatus automatically stops the engine under certain conditions and subsequently automatically restarts the engine if it is determined that the brake booster pressure has fallen below a predetermined value. The engine control apparatus also effects such automatic restarting if a predetermined maximum time interval has elapsed since the automatic engine stop occurred. This ensures that even when the booster pressure value cannot be reliably obtained after an automatic engine stop has occurred, the engine will be restarted before the booster pressure falls excessively.