A power transmission device of the invention is provided with an engine, a motor, and an oil pump which is connected through a one-way clutch to the rotating shaft of the engine and to the rotating shaft of the motor. When starting the engine (S10-Y), the motor is rotated at a speed which is higher than a speed corresponding to the speed of the engine and which is lower than a speed corresponding to the idling speed of the engine (S40). When the temperature of the engine is low, the speed of the motor at which the motor drives the oil pump during the start of the engine can be set higher than the speed of the motor when the temperature of the engine is high.