A slip of drive wheels of a vehicle driven via a continuously variable transmission is suppressed due to fuel cut of a multi-cylinder engine. The speed change response characteristics of the transmission are made to vary according to the engine rotation speed when fuel cut is performed. A speed change ratio command value is calculated from a target speed change ratio based on a first-order delay due to a predetermined time-constant. The response of the transmission is thus delayed for low engine rotation speed than for high rotation speed, and undesirable fluctuation of the speed change ratio when the drive wheels slip is prevented.