A controller (an engine controller 100) feeds a fuel into a cylinder 11 through a fuel feeder (including a fuel injection valve 53 and a fuel feeding system 54) when the cylinder 11 is in an intake stroke and a compression stroke and if an engine body (an engine 1) is both in a cold running phase and under a heavy load. The engine body at or below a predetermined temperature is in the cold running phase. The load applied to the engine body is heavy when the engine body is under at least a predetermined load. The controller also lowers the upper limit of the charging efficiency of the engine body as the vaporization rate of the fuel fed into the cylinder decreases.