A vehicle driving system control apparatus includes a power transmission device and a power transmission control section. The power transmission device includes an engine input shaft, a motor input shaft, an output shaft, an engine-side gear mechanism transmitting a power of the engine input shaft to the output shaft, a motor-side gear mechanism transmitting a power of the motor input shaft to the output shaft, a first clutch enables and disables a power transmission between the engine input shaft and the motor input shaft, a second clutch enables and disables a power transmission between the motor-side gear mechanism and the output shaft, and a third clutch enables and disables a power transmission between the engine-side gear mechanism and the output shaft. The power transmission control section determines statuses of the clutches and required torques of motor generators in correspondence with a rotation speed of an axle.