A power transmission device mounted on a vehicle in which operation of an engine is stopped when vehicle speed has been reduced to a predetermined vehicle speed. The device includes an oil pump driven by the engine; a hydraulic control device regulating pressure from the oil pump; a continuously variable transmission mechanism in which groove widths of a primary pulley and a secondary pulley are set by hydraulic pressure from the hydraulic control device; a hydraulic engagement element engaged by hydraulic pressure from the hydraulic control device to couple the continuously variable transmission mechanism to the engine; a clamping pressure sensor that detects clamping pressure of a belt of the continuously variable transmission mechanism; and a control device disengaging the hydraulic engagement element when the detected clamping pressure of the belt reaches less than or equal to a threshold value after operation of the engine is stopped.