An engine automatic stop and start system monitors a booster negative pressure and a braking operation. A combination of the booster negative pressure and the brake operation can effectively indicate that a booster negative pressure will be insufficient to ensure a brake function. The controller evaluates the booster negative pressure and the brake operation, and restarts the engine when it is estimated that the booster negative pressure may be decreased below a threshold. As a result, it is possible to restart the engine before the booster negative pressure is decreased.