A control device for a compression-ignition engine is provided, which includes an engine having a plurality of cylinders, spark plug, a fuel injector, and a control unit connected to the spark plug and the fuel injector. The control unit causes the engine to perform an all-cylinder operation when the engine operates at a load above a given load, and perform a reduced-cylinder operation at a load below the given load. In the reduced-cylinder operation, the fuel injector injects fuel to one or some of the cylinders to generate mixture gas, the spark plug ignites the mixture gas, and the engine starts, at an air-fuel ratio larger than a stoichiometric air-fuel ratio and a large compression ratio, SI combustion in which the mixture gas is ignited to combust by flame propagation, and then perform CI combustion in which unburned mixture gas ignites by self-ignition.