To prevent generation of vibration by approximating the time variance rate of engine speed to a constant value in stopping an engine.

An air-conditioning compressor 20 capable of being driven by the power of the engine 10 or a motor 18 is installed on a belt 12 through an electromagnetic clutch 16. The rotational angle of the engine 10 is detected by a crank angle sensor 28. In stopping the engine 10, the torque effected on deceleration by the compressor 20 is given during the period of such a rotational angle that the time variance rate of the engine speed is smaller than its criterion, and the torque effected on acceleration by the motor 18 is supplied during such a period that the time variance rate of the engine speed is larger than the criterion, thus preventing vibration of the engine speed.