Coast stop vehicle and control method thereof

An oil pump (10m) driven by an engine (1) generates a hydraulic pressure supplied to a frictional engagement element (32). An accumulator (35) provided at an intermediate position of an oil path supplies the hydraulic pressure generated by the oil pump (10m) to the frictional engagement element (32). A controller (12) stops the engine (1) after a hydraulic pressure reducing condition to reduce the hydraulic pressure supplied to the frictional engagement element (32) holds and the hydraulic pressure supplied to the frictional engagement element (32) is reduced.