An idling stop control of the invention attains an auto start and an auto stop of an engine. At a time point t1, pre-set stop conditions are met to cut off a fuel supply to the engine. Preset starting conditions may be met at a time point t2 when the engine still continues rotating in a normal direction by the inertial force. In this state, the idling stop control starts cranking the engine. The preset starting conditions may be met at a time point t4 when a piston does not complete a compression cycle immediately before a stop of the engine but is pressed back by the compressed air to rotate the engine in a reverse direction. In this state, the idling stop control waits until cancellation of the reverse rotation of the engine and then starts cranking the engine. The arrangement of the invention desirably ensures a quick start of the engine, while effectively preventing an excess stress from acting on a gear mechanism, which connects a starter motor to the engine.