To continue fuel cut control over a long period similarly to a case of having no auxiliary machine load, even when the auxiliary machine load is caused.

This control device performs the fuel cut control when a return determining rotating speed for determining the resumption of fuel supply to an internal combustion engine in a state of having no driving request to the internal combustion engine, is a predetermined return rotating speed or more, by connecting a transmission to the output side of the internal combustion engine connected with an auxiliary machine, and includes a rotating speed predicting means (Step S5) for predicting a rotating speed after a predetermined time of the return determining rotating speed, and a down-shift indicating means (Step S6 and S8) for performing a down-shift for increasing the gear ratio of the transmission in a state of stopping the load by the auxiliary machine when determining that the predicted return determining rotating speed becomes a predetermined return rotating speed or less as a rotating speed for resuming the supply of fuel.