Apparatus and method for controlling a four-wheel drive vehicle

In case there occurs a wheel slip in either one of front left and right wheels or rear left and right wheels, a traction control through an engine output and a traction control through braking are implemented. Furthermore, in case the vehicle speed is slow, a final limited slip differential torque is set by adding a limited slip differential compensation amount according to a steering angle to a limited slip differential torque set according to an inputted torque and a front/rear differential rotation, and further adding thereto a limited slip differential compensation amount according to the vehicle speed for increasing the compensation.