At the start-up of an engine, the ignition timing and the air-fuel ratio are controlled to prevent overload onto the volume of ISC air and decreased torque and torque difference.The fuel condition based on the amount of ignition timing correction to inhibit rotational fluctuation during idling is determined and the fuel quantity based on the result is corrected.Right after an engine has started and until a pilot burner is created in the heat spot of the catalyst, the ignition retard control is mainly executed, and at the time when it is determined that a pilot burner has been created in the catalyst's heat spot, the lean air-fuel ratio control is to be executed instead of the ignition retard control. Furthermore, when the ignition retard control changes to the lean air-fuel ratio control, the state transition control is executed along the equivalent ISC air volume line so as not to cause torque fluctuation.