A spark-ignition direct injection engine is provided. The engine includes an engine body, a fuel injection valve, a fuel pressure setting mechanism, an ignition plug, and a controller. The controller switches between a compression-ignition mode where the engine body is operated to perform compression-ignition combustion and a spark-ignition mode where the engine body is operated to perform spark-ignition combustion. Immediately after switching from the spark-ignition mode to the compression-ignition mode, the controller operates the engine body in a compression-ignition initial mode where the fuel pressure is set to be 30 MPa or above and the fuel injection valve is controlled to perform the fuel injection in a period from a late stage of the compression stroke to an early stage of the expansion stroke so that the gas mixture self-ignites to combust.