A control apparatus for a direct-injection, spark-ignition engine including a temperature-condition detector for detecting a temperature condition of the engine catalyst, and a controller for controlling a fuel-injection operation. The controller controls the fuel injector to perform divided fuel injections of at least a leading fuel injection and a trailing fuel injection during a compression stroke prior to the ignition timing based upon a detection of the temperature condition in an inactivated state of the catalyst, the trailing fuel injection being performed at such a timing that its mixture concentrates adjacent to the spark plug at the ignition timing by way of high cylinder pressure during a late-stage of the compression stroke, the leading fuel injection being performed at such a timing that its mixture distributes around a mixture layer by the trailing fuel injection at the ignition timing, and a midpoint between an initiation of the leading fuel injection and an initiation of the trailing fuel injection being positioned within a period during a latter half of a compression stroke.