PURPOSE: To perform supercharging without the occurrence of a delay in response and to improve starting performance and low speed running perfor mance of an engine without worsening fuel consumption, by a method wherein, during low rotation high load running of an engine, a first on-off valve is closed and a second on-off valve is opened.

CONSTITUTION: During low rotation, low and middle load running, an electromag netic clutch 9 is connected, and with a first on-off valve 15 closed, a second on-off valve 17 is opened to feed supercharged air to an engine 1 by means of a mechanical type supercharger 10. Further, when, during high load running, a boost pressure is needed, the first on-off valve 15 is closed and the second on-off valve 17 is closed, air delivered from the mechanical type supercharger 10 is fed to the suction port of a blower 6 of a turbosupercharger 4, and super charging by the turbosupercharger 4 is effected. When the number of revolutions is also changed, the electromagnetic clutch 9 of the mechanical type super charger 10 is turned OFF when a pressure between the mechanical type super charger 10 and the turbosupercharger 4 produces negative pressure.