A vehicle driving system includes a pulley shaft synchronously rotating with a crankshaft of an engine, an auxiliary unit drive shaft driving an auxiliary unit, a planetary gear mechanism portion having elements such as a sun gear, a pinion carrier and a ring gear. The pulley shaft and the auxiliary unit drive shaft are adapted for connection to any two of the elements, respectively. The motor connecting to the remaining element of the planetary gear mechanism portion. A lock-up clutch connecting together the two or more elements of the planetary gear mechanism portion. A one-way clutch for restricting the rotation of the auxiliary unit drive shaft in one direction, wherein the planetary gear mechanism portion, the motor, the lock-up clutch, and the auxiliary unit drive shaft are coaxially disposed in line.