When a predetermined restart condition is satisfied after an engine is automatically stopped, whether or not a piston of a stopped-in-compression-stroke cylinder which is in a compression stroke falls within a specific range set at a bottom dead center side of a predetermined upper limit position is determined. When the piston of the stopped-in-compression-stroke cylinder falls within the specific range, a first compression start is executed in which fuel is injected from an injector into the stopped-in-compression-stroke cylinder for the first time and is then self-ignited. In the first compression start, a start timing of a first fuel injection operation with respect to the stopped-in-compression-stroke cylinder is set to be earlier as a stop position of the piston of the cylinder gets closer to the bottom dead center within the specific range.