An apparatus comprises a changeover mechanism which is able to change a connection state of an electric motor output shaft to any one of “an IN-Connection State” in which a power transmission path is provided between a transmission input shaft and the electric motor output shaft, “an OUT-Connection State” in which a power transmission path is provided between the transmission output shaft and the electric motor output shaft, and “a neutral state” in which no transmission path therebetween is provided. When a kick-down-condition is satisfied, a changeover operation for changing an electric motor connection state to the OUT-Connection State is firstly performed. Thereafter, a gear position shifting operation for increasing a transmission reduction ratio is performed. After the kick-down-condition satisfied, an E/G side output torque Te and a M/G side output torque Tm is adjusted in such a manner that a sum Ts of Te and Tm continues to increase.