A steering control apparatus for a vehicle having a power source for generating power, and drive shafts for transferring the power to driving wheels of the vehicle, and a traction control device for controlling braking torque applied to the wheels. The apparatus comprises a detection device for detecting the braking torque applied to the wheels, a calculation device for calculating a driving force difference between the wheels, on the basis of the detected braking torque, a power source state detection device for detecting an actuating state of the power source, and a control device for controlling steering torque created by the steering wheel, and applying torque steer reducing torque to the steering wheel. A desired value of the torque steer reducing torque is determined, based on the driving force difference and the actuating state of the power source. And, the torque steer reducing torque is applied to the steering wheel, according to the desired value of the torque steer reducing torque, to reduce the torque steer.