A control device for a vehicle continuously variable transmission comprises a shift control means for controlling either of or both the speed ratio at the continuously variable transmission mechanism and the gear position at the subtransmission mechanism so as to adjust an overall speed ratio to a final speed ratio and a torque capacity control means for controlling the torque capacity at a disengagement-side frictional engagement element in the subtransmission mechanism so as to sustain a torque capacity value substantially equal to zero in an inertia phase occurring during a process of adjusting the gear position at the subtransmission mechanism from the first gear position to the second gear position when a negative torque is input to the vehicle continuously variable transmission.