The invention is provided with an ignition control section and an injection control section. When partial compression ignition combustion is carried out, the ignition control section causes an ignition plug to carry out: main ignition in which a spark is generated in a late period of a compression stroke or an initial period of an expansion stroke to initiate SI combustion; and preceding ignition in which the spark is generated at earlier timing than the main ignition. Also, when the partial compression ignition combustion is carried out, the injection control section causes an injector to inject fuel at such timing that the fuel exists in a cylinder at an earlier time point than the preceding ignition. Timing of the preceding ignition is set to be more retarded when an engine speed is high than when the engine speed is low.