A control device of a spark-ignition engine is provided. The control device includes a main body of the engine, a fuel injection valve, an ignition plug, and a controller. According to an engine operating state, the controller switches between a compression-ignition mode in which compression-ignition combustion is performed, and a spark-ignition mode in which spark-ignition combustion is performed. The controller switches from the spark-ignition mode to the compression-ignition mode by performing in order, a first stage where an air-fuel ratio of mixture gas is set to a predetermined value and the spark-ignition combustion is performed, a second stage where the air-fuel ratio of the mixture gas is set leaner than the first stage and the compression-ignition combustion is performed, and a third stage where the air-fuel ratio of the mixture gas is set richer than the second stage and the compression-ignition combustion is performed.

A control device of a gasoline direct-injection engine is provided. The control device includes an engine body, an injector, and a controller. Within a high load operating range, the controller causes the injector to perform a pre-injection and a post injection. In the pre-injection, the fuel is injected to cause a fuel concentration within an in-cylinder radially peripheral section to be higher than a fuel concentration within an in-cylinder radially central section at a timing for the fuel to ignite. In the post injection, the fuel is injected to cause the fuel concentration within the radially central section to be higher than the fuel concentration within the radially peripheral section at a timing for the fuel to ignite. The timing for the fuel injected in the post injection to ignite is after an oxidative reaction of the fuel injected in the pre-injection occurs and after a compression top dead center.