In a continuously variable transmission, a speed change control device includes a vehicle speed sensor, a brake sensor, a release vehicle speed memory which, when the brake is operated, renews and stores the brake release vehicle speed, and a gradient sensor for detecting a running road gradient. When, in an engine brake running state, the present vehicle speed is higher than the brake release vehicle speed stored in the release vehicle speed memory, a speed change target value is obtained according to the difference between the present vehicle speed and the brake release vehicle speed and to the road gradient. And, when, in the same state, the present vehicle speed is lower than the brake release vehicle speed, the speed change target value is obtained according to the road gradient. The speed change control is carried out so as to obtain the speed change target value.