An auxiliary injection is carried out at an in-cylinder temperature at which a premixed combustion by the auxiliary injection is separatable into a low-temperature oxidation reaction and a high-temperature oxidation reaction, in a compression self-igniting internal combustion engine in which fuel injected into a cylinder from a fuel injection valve combusts in the cylinder, and that is configured to carry out an operation of fuel injection from the fuel injection valve. The operation of fuel injection includes at least a main injection and the auxiliary injection. The main injection causes a combustion mainly including a diffusion combustion in the cylinder. The auxiliary injection is carried out prior to the main injection and causes a combustion mainly including the premixed combustion in the cylinder. Specifically, an in-cylinder gas temperature (750K) is used as a reference, and the auxiliary injection is carried out before the in-cylinder gas temperature reaches 750K, so as to separate the low-temperature oxidation reaction and the high-temperature oxidation reaction from one another. This control makes the premixed combustion slow before a compression top dead center is reached, and ensures control of the premixed combustion in a temperature controlled manner in accordance with the transition of the in-cylinder gas temperature. This ensures unambiguous determination of the injection time of the auxiliary injection based on the in-cylinder temperature, and facilitates the attempt to simplify the fuel injection control.