A differentiator calculates the acceleration of the rear wheels. An acceleration threshold calculation means enable the skid-detection acceleration threshold to be adjusted corresponding to the conditions of the vehicle. An acceleration skid-detection means make a comparison between the acceleration of the wheels obtained by the differentiator and the skid-detection acceleration threshold adjusted by the acceleration threshold calculation means, and determine whether or not a skid of the wheels has occurred, based upon the comparison result. Such an arrangement provides a vehicle driving force system having a function of detecting a skid even in a case that a skid of the wheels has occurred at a low acceleration of the vehicle.