To alleviate vibration and shock by gradually reducing a fuel injection amount to be injected in an engine stopping mode after switchover to the off position of a starting operation means in correspondence to the elapse of time of the engine stopping mode.

After determining whether the ignition key for starting or stopping an engine has been turned from the on position to the off position (S1), if the ignition key is in the off position a control mode shifts to an engine stopping mode. For stopping the engine, a fuel injection reduction amount Qd which becomes larger in correspondence to the elapse of time from the switchover to the off position is calculated, and the control mode enters an engine-stop starting mode (S2). A fuel injection amount at the engine-stop Qf in the engine- stop starting mode becomes an amount to decrease in correspondence to the elapse of time as a result of deduction of the fuel injection reduction amount Qd from an engine-stop starting fuel injection amount Qfs. Consequently, engine speed decreases. In this case, an EGR valve is closed, the depression amount of an accelerator pedal is set to zero, an idling adjustment is suspended, and a duty ratio of an intake throttle valve is retained at the on position.