PURPOSE: To drive a supercharger, which has an intake and an exhaust by-pass valves, at the optimum condition all the time, by detecting the rotational frequency of an engine and the supercharger to control the by-pass valves on the basis of data corresponding to the detected rotational frequency.

CONSTITUTION: A control circuit 100 made of a microcomputer fulfills its function depending on each task level on the basis of inputs from a hot-wire-type flow meter 24, a crank angle sensor 42, a knock sensor 44, a λ sensor 46 and a compressor's rotational frequency detector 65. The quantity of compensation of an exhaust by-pass valve 68 depending on the intensity of knocking is controlled in terms of a value counted by a counter in the control circuit 100. The degree of opening of the exhaust by-pass valve 68 not under acceleration and that of an intake by-pass valve under knocking area are controlled by referring to a characteristic table stored in a memory in terms of the rotational frequency of a supercharger.