In order to suppress NVH under an admissible value during high speed rotation in a compression-ignition engine, the invention provides a control device of a compression-ignition engine, which comprises a spark plug (25) and a controller (10). The controller (10) performs SPCCI combustion of making unburnt mix gas burn through automatic ignition after the spark plug (25) ignites the mixed gas and make the gas burn. The controller (10) increases a heat ratio through a heat ratio changing section (102a) at a higher speed of an engine with respect to a lower speed.