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. Within a low engine speed operating range of a predetermined high engine load range, the fuel pressure setting mechanism sets a fuel pressure to 30 MPa or above, the fuel injection valve injects fuel between late stage of compression stroke and early stage of expansion stroke, and the ignition plug performs spark-ignition after the fuel injection completes. Within a high engine speed operating range of the high engine load range, the fuel injection valve injects fuel between intake stroke to mid-stage of compression stroke, and the ignition plug performs the spark-ignition. The ignition timing is changed according to an octane number, the changing width of the ignition timing is shorter within the low engine speed range than the high engine speed range.