A coast stop vehicle includes a variator which continuously changes a speed ratio by changing a winding diameter of a belt mounted on pulleys, a sub-transmission mechanism connected in series with the variator and shifting discrete gear positions by changing engaged states of a plurality of frictional engagement elements, and a coast stop unit which stops the rotation of the drive power source and releases the engaged frictional engagement element when the coast stop condition holds during travel. The coast stop unit includes a coast stop prohibiting unit which prohibits the coast stop regardless of the coast stop condition when it is predicted at the time of determining whether or not the coast stop condition holds that a belt tightening force of the pulley falls below an engaging force of the frictional engagement element in the engaged state by the execution of the coast stop.