Provided is 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. Ignition timing of the preceding ignition is set to be more advanced when an in-cylinder temperature specified by an in-cylinder temperature specification section is high than when the in-cylinder temperature is low.