To prevent the undesirable acceleration of a vehicle during the shift change of a transmission at a downward grade in a vehicle power transmission.

In a vehicle power transmission 10, a fuel control engine 2 is connected to an input shaft 20 of a transmission 14 through a master clutch 16, and a terminal driving device 24 and a driving wheel 24 are connected to an output shaft 22 through a driving shaft 22A. A retarder 28 is mounted on the driving shaft 22A. A control unit 30 increases the speed reducing torque of the retarder 28 when the output torque of the fuel control engine 12 is negative and the vehicle acceleration is positive during the shift change of the transmission 14 to a target gear ratio, maintains a speed reducing torque at the time of zero and reduces the speed reducing torque at the time of negative. With speed reducing torque by the retarder 28 thus imparted appropriately to the driving shaft 22A, the undersirable acceleration of a vehicle during shift at a downward grade can be prevented.