To easily construct a system for feed back control by executing feed back control treatment by response designating control capable of variably designatable damping speed of a deviation between real rotating speed and target rotating speed of an internal combustion engine in association with a value of a predetermined parameter.

It is judged whether a mode is a start mode of an internal combustion engine 1 or not, and a command value of a fuel supplying amount is generated per control cycle by a controller 2 in the case where it is not the start mode. After it is judged whether there is a necessity for performing a control process of a FIRE mode for activating a catalytic device 3 in an early stage or not, a bypass opening of a flow rate control valve interposed in a bypass passage for bypassing a throttle valve is controlled through an actuator 24. An ignition timing and a command value is generated. Feed back control process is executed by means of response designating control capable of variably designatable damping speed of a deviation between real rotating speed and target rotating speed of an engine by a predetermined parameter value, and thereby, control accuracy is improved.