A main injection of fuel from a fuel injector into a combustion chamber is made to auto-ignite. During the compression stroke after the main injection and before the auto-ignition of the fuel injected during the main injection, a first auxiliary injection and a second auxiliary injection are successively injected from the fuel injector. By controlling the injection timing of the first auxiliary injection, the ignition timing of a spark plug, and the injection timing of the second auxiliary injection, the fuel injected during the first auxiliary injection is made to burn by flame propagation combustion by the ignition action of the spark plug, the fuel injected during the second auxiliary injection is made to be injected inside the flame propagation combustion region, and the fuel injected during the second auxiliary injection is made to burn by diffusive combustion before auto-ignition of the fuel injected during the main injection occurs.