In the present invention an engine control unit (ECU) controlling a continuously variable transmission (CVT) installed in an automobile continuously changes the transmission gear ratio of the CVT, and changes the transmission gear ratio so as to perform upshifting in a stepwise fashion. When the accelerator opening degree is constant, the allowable number of instances of stepwise upshifting is increased as the accelerator opening degree increases. Thus, the vehicle acceleration and the vehicle engine noise can be changed suitably in accordance with the driver's intention to accelerate, and the drivability of a vehicle equipped with a continuously variable transmission can be further improved.