An upper part of FIG. 7 represents a catalyst warming-up control when a normal fuel is used, and a lower part of FIG. 7 represents the catalyst warming-up control when a heavy fuel is used. As understood from a comparison between the upper part and the lower part of FIG. 7, the start timing of the ignition period and the total injection amount of the injector in each cycle when the heavy fuel is used are the same as those when the normal fuel is used, though the ratio of the intake stroke injection and the expansion stroke injection to the total injection amount of the injector is changed to increase the fuel amount of the expansion stroke injection as compared with the case where the normal fuel is used.