With rapid development of the automobile industry and the growing maturity of the automotive electronic technologies, the distributed-traction electric vehicle with four-wheel-distributed steering/braking/traction systems is considered to be an important development direction. With its unique chassis structure, it is the ideal benchmark platform sued to evaluate active safety systems. The distributed-traction electric vehicle with four-wheel-distributed steering system is essentially full drive-by-wire vehicle. With its flexible chassis layout and high control degrees-of-freedom, the full drive-by-wire electric vehicle acted as a kind of redundant system is an ideal platform for the research of integrated control. In this treatise, the longitudinal dynamics of the electric vehicle as well as its lateral and yaw motions are controlled simultaneously. In the motion control layer, the total force and total torque of the vehicle motion control are obtained by using the sliding model controller, and the elimination of chatter is achieved by using the terminal sliding model control technique for the yaw motion control. In the tire force allocation layer, the axial load transfer issue is taking into consideration during the process of tire force distribution, and then, the optimal allocation problem is transformed into a quadratic programming issue with constraint. In the executive layer, the target tire force output from the tire force allocation layer are ultimately achieved by controlling the drive/braking torque of the wheel motor and the steering angle of steering motor. The results demonstrate the effectiveness of the designed controller and it is shown via the co-simulation of CarSim and MATLAB/Simulink that the proposed control algorithm is able to coordinating with drive and steering system better, in which the electric vehicle can track the target vehicle and ideal yaw rate.