A coast stop vehicle which executes coast stop control for stopping an engine during the travel of a vehicle, is provided with a frictional engagement element provided between the engine and a driving wheel, a first deceleration calculating unit which calculates first deceleration, which is rotation deceleration of a rotation shaft on the driving wheel side of the frictional engagement element, and an engagement-state control unit which controls an engagement state of the frictional engagement element so that decrease of the engine rotation speed is suppressed on the basis of the first deceleration while the coast stop control is executed.