To accurately set timing for changing a supply oil pressure increase rate to a starting clutch in an engine restart for eliminating a time delay and a shock.

A power transmission device is constructed of an engine E, a torque converter TC, and an automatic transmission TM. This engine restart departure controller calculating pump absorption torque of the torque converter is provided with a solenoid valve capable of setting the oil pressure increase rate of an oil pressure supplied to the starting clutch. When the engine is restarted from an engine stopping condition and working oil is supplied to a frictional engagement element to engage it for setting a starting gear, oil pressure increasing at a first oil pressure increase rate is supplied to the frictional engagement element until the calculated pump absorption torque reaches a predetermined determination value, and after the calculated pump absorption torque reaches a predetermined determination value or more, oil pressure increasing at a second oil pressure increase rate lower than the first oil pressure increase rate is supplied.