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.