A steering control apparatus is provided for a vehicle having a steering wheel for steering steered wheels of the vehicle, a power source for generating power, and drive shafts for transferring the power to the steered wheels, to be served as driving wheels of the vehicle. The apparatus comprises an accelerating operation detection device for detecting accelerating operation amount by a vehicle driver, and a steering torque control device for controlling steering torque created by the steering wheel, and applying torque steer reducing torque to the steering wheel. The steering torque control device is adapted to reduce torque steer, which is transiently created on the steering wheel due to characteristics of the drive shafts, when the accelerating operation amount detected by the accelerating operation detection device becomes equal to or greater than a predetermined value.