A first supercharger and a second supercharger which is larger in size than the first supercharger are disposed in series in intake and exhaust passages. In a region B in which both the supercharging effects of the first and second superchargers are utilized, the opening of an exhaust control valve disposed in a passage for bypassing the turbine of the first supercharger is set to an intermediate degree, and the opening of an intake control valve disposed in a passage for bypassing the compressor of the first supercharger is set to the minimum. In a region C in which the supercharging effect of only the second supercharger is utilized, both the openings of the exhaust control valve and the intake control valve are set to the maximum. When the control region shifts from region B to region C as aresult of acceleration of the vehicle, the fuel injection amount is reduced over a predetermined period immediately after the shift. Occurrence of a "momentary increase in the output torque of the internal combustion engine stemming from a sharp drop in the exhaust pressure" which may occur as a result of the shift can be restrained, and a torque step which a passenger may feel can be reduced.