A control system of a continuously variable transmission for a vehicle compensates for delays in an estimated input torque TINE based on a gradient value (variation) of the estimated input torque TINE,. For example, a friction force being applied to a driving belt of a continuously variable transmission is regulated according to the compensated estimated input torque TINE. Accordingly, an appropriate torque transmitting capacity is maintained in the transmission even at a rapid accelerating operation of the vehicle, while realizing good fuel efficiency.