A homogeneous charge compression ignition engine that prevents knocking and misfires when changing output and when the load or air-fuel ratio changes due to one reason or another when operating under a predetermined condition. A controller determines whether or not the air-fuel ratio is changing in such a manner that there is a possibility of knocking or misfires occurring by using a map defining a range, in which stable homogeneous charge compression ignition operation is enabled, in relation with the air-fuel ratio and the intake air temperature. When the air-fuel ratio indicates that there is a possibility of knocking or misfires occurring, the controller controls an intake air temperature adjustor to adjust the intake air temperature based on the map.