An apparatus for controlling an continuously variable transmission (CVT) used for a power transmission system of a vehicle. The CVT is controlled such that an actual engine speed becomes a desired engine speed. The desired engine speed is set as a function of running parameter such as intake throttle position. When the CVT is controlled in the same way as at the steady state of the vehicle at the acceleration of the vehicle, the acceleration performance is degraded. Thus, according to the present invention, the speed ratio of the CVT is reduced when the acceleration of the vehicle is small, in spite of the requisition of the vehicle acceleration. As a result, satisfactory drivability is attained.