A homogeneous charge compression ignition engine includes a combustion chamber and a piston for compressing and igniting an air-fuel mixture in the combustion chamber. A variable valve actuation mechanism opens and closes an exhaust valve to perform internal exhaust gas recirculation. A heater heats the mixture before the mixture is supplied to the combustion chamber. A storage device stores correspondence information of the amount of internal exhaust gas recirculation and heated state of the mixture heated by the heater that are necessary to perform homogeneous charge compression ignition in relation with the load of the engine and the rotation speed of the output shaft. A controller controls the variable valve actuation mechanism and the heater to achieve the amount of internal exhaust gas recirculation and heated state of the mixture in correspondence with the load and speed required for the engine.