A rotational driving force from an engine E in a fuel-supply termination control is transmitted through a continuously variable transmission CVT, and this transmission of the rotational driving force is controlled by the engagement of a starting clutch 5. In this arrangement, a control system terminates the fuel supply to the engine at the elapse of a predetermined time from the starting of a deceleration of the vehicle. When the control system detects that the throttle of the engine has closed, it reduces the engaging force of the starting clutch 5 to disengage the clutch into a pre-engagement condition. Thereafter, when the fuel supply to the engine is terminated, the engaging force is gradually increased to bring the starting clutch 5 gradually into engagement.