A method of controlling a continuously variable transmission which includes a fixed pulley member and a movable pulley member supported relative to the fixed pulley member so as to be movable both toward and away from the fixed pulley member, including the steps of decreasing and increasing the width of a groove defined between the pulley members to thereby respectively increase and decrease a rotational radius of a belt which is received between the pulley members in the groove. When a target engine rotational speed based on throttle opening degree and vehicle velocity changes during vehicle running, a transient speed change control is performed so as to change a belt ratio of the transmission based on a predetermined rate limit value. A control unit is provided for receiving the throttle opening degree and vehicle velocity and executing the transient speed change control. During execution of the transient speed change control, the rate limit value is changed in accordance with the throttle opening degree and vehicle velocity, the throttle opening is changed on the basis of vehicle velocity, and the final target engine rotational speed is changed on the basis of the rate limit value. A time limit for execution of transient control is set on the basis of the throttle opening degree and the vehicle velocity.