Idle stop control method and control device

There is provided an idle stop system that can more quickly restart with small noise in conducting idle stop. In preparation for a restart request during an engine inertial rotation, after a motor is rotated in a state where a starter motor is not coupled to the engine, a pinion is engaged with a ring gear 204 during the motor is subjected to inertial rotation like the engine. In this situation, the rotational speed including future pulsation of the engine is estimated with the use of information on the crank angle, and a pinion pushing timing is controlled so that the pinion and the ring gear 204 contact each other with a given rotational speed difference taking a delay time of a pinion pushing unit into consideration.