PURPOSE: To obtain an excellent supercharging effect over the entire speed range of engine operation, by providing a first intake valve for feeding non-supercharged air and a second intake valve opened with some delay to the first intake valve and closed during the compression stroke of an engine in the cylinder head of the engine.

CONSTITUTION: A first intake valve 25, a second intake valve 26 and an exhaust valve 30 are provided in an engine body 29, and the intake valves 25, 26 are provided respectively in a first and a second intake passages 22, 24. The first intake pipe 22 is connected directly to an air-flow meter 20 while the second intake pipe 24 is connected to the air-flow meter 20 by the intermediary of a compressor 23 of a small supercharger 27. Further, the exhaust valve 30 and a silencer 35 are connected together via a first exhaust pipe 31 having a turbine 28 of the supercharger 27 and a second exhaust pipe 33 having an exhaust-gas by-pass valve 32. Here, arrangement is such that the first intake valve 25 is opened during the suction stroke of an engine while the second intake valve 26 is opened with some delay to the first intake valve 25 and closed during the compression stroke of the engine.