An engine body includes a cylinder with a geometrical compression ratio of 15 or higher, and is supplied with fuel containing at least gasoline. When an operating mode of the engine body is in a high load range, a controller (i.e., a PCM 10) drives a fuel injection valve (i.e., an injector) 67 to inject the fuel at a time within a retarded period between a terminal stage of a compression stroke and an initial stage of an expansion stroke in a low speed range. The controller drives the fuel injection valve to inject the fuel in an intake stroke until an intake valve 21 is closed in a high-load high-speed range.