To provide a control device of a continuously variable transmission for a vehicle at low cost, preventing a belt slip at a reverse start on the down grade.

When a vehicle speed is smaller than or equal to a prescribed value and an accelerator opening is smaller than or equal to a prescribed value in a reverse range, closing control of a primary pulley oil chamber of the continuously variable transmission is executed. When the vehicle speed is smaller than or equal to the prescribed value, the accelerator opening is larger than the prescribed value, and moreover, a brake is OFF in the reverse range, clamping pressure increasing control for increasing the belt clamping pressure of the continuously variable transmission by a prescribed value in accordance with the accelerator opening, is executed. By executing such two-stage control, the belt slip at the reverse start is prevented.