A supercharged engine has a geometric compression ratio ser to 16 or more and is designed to perform a compression self-ignition combustion under an air-fuel ratio leaner than a stoichiometric air-fuel ratio at least in a low engine speed range. On a lower engine load side than a given engine load within an engine operating region at which the compression self-ignition combustion is performed, a fresh air amount is reduced and an effective compression ratio (ε′) is increased, as compared with a higher engine load side than the given engine load within the engine operating region, and, on the higher engine load side than the given engine load, a supercharging pressure based on a supercharger (25) is increased to increase the fresh air amount, and the effective compression ratio (ε′) is reduced, as compared with the lower engine load side than the given engine load. This makes it possible to perform the compression self-ignition combustion under a lean air-fuel ratio in a wider engine load range to effectively enhance engine thermal efficiency, while eliminating a need for an operation of forcedly raising/lowering a temperature of fresh air.