A driving force control system for a four-wheel drive vehicle[is disclosed] which enables the vehicle to smoothly start on a low-.mu. road surface, and is capable to distributing just required amounts or driving forces to auxiliary drive wheels depending on an actual accelerating condition of the vehicle, thereby improving the response and fuel economy of the vehicle. The four-wheel drive vehicle includes front wheels as main drive wheels, and rear wheels as auxiliary drive wheels. The driving force control system controls engagement forces of electromagnetic clutches to thereby control the driving forces (torques) distributed to the rear wheels. The 2/4WD.multidot.ECU of the driving force control system calculates a filtered vehicle acceleration XGF1F of the vehicle 2 based on a drive torque TD, and then calculates a basic VATC torque value VATC based on the calculated filtered vehicle acceleration XGF1F, for use in calculation of the final desired VATC torque value TOBJM of torque to be distributed to the rear wheels.