To improve the limits of knocking due to a decreased compression ratio for high power while keeping an expansion ratio to the extend of realizing good thermal efficiency by additionally arranging a supplied air cooler in a supply port for a miller cycle engine of which the compression ratio is decreased by delaying a valve closing timing for a supply valve.

Supply mixture mixed with an air/fuel mixer 1 is compressed at the blower portion 2a of a supercharger 2, cooled by a supplied air cooler 3, adjusted in amount by a throttle 4 and supplied from a supply port 5 to cylinders. When such a supercharged gas engine is operated as a miller cycle engine of which the compression ratio is decreased by delaying a valve closing timing for a supply valve, a knocking limit load factor is reduced as a temperature at the exit of the throttle is higher, and so the second supplied air cooler 6 in a small size is additionally arranged near the supply port 5. In this way, temperature rise at the exit of the throttle and in the supply port 5 following the delay of a valve closing timing for the supplying valve is restricted and the knocking limit load factor is improved.