The characteristics of flexible and controllable torque of each wheel is available for the four in-wheel motor independent-drive vehicle(4MIDV). Through the adjustment of the four in-wheel motor driving and braking torque, the yaw moment control can be realized rapidly without losing the power of the vehicle, and thereupon improves the steering stability. A hierarchical steering stability control strategy based on the LQR optimal control and the optimal control allocation algorithm is proposed in this paper. The upper controller adopts the LQR optimal control method to realize the compensating yaw moment control. The bottom controller is attributed as two kinds of torque allocation algorithms: the torque average allocation algorithm and the optimal torque allocation algorithm based on the objective function of minimizing the control allocation error and the control energy consumption. The effect of this proposed control strategy is verified through the joint simulation of CarSim and Matlab/Simulink when the double lane change experiment is conducted for the vehicle in the extreme condition of the low tire-road friction coefficient. The simulation results show that compared to no control applied, the proposed control strategy can greatly improve the steering stability of the vehicle. In addition, compared to the torque average allocation algorithm, the optimal torque allocation algorithm based on the objective function enables the steering stability of the vehicle to be further improved.