A coast stop vehicle which stops an engine during the travel of the vehicle is provided with a variator including a pair of pulleys and a belt mounted between the pulleys and capable of continuously changing a speed ratio. A controller judges whether or not coast stop conditions to stop the engine during the travel of the vehicle hold, stops the engine when the coast stop conditions hold, and prevents the speed ratio from being upshifted to a higher side than a speed ratio at the time of starting the coast stop control during the coast stop control.