Compared with the traditional front-wheel- steering (FWS) vehicles, four-wheel-independent-steering (4WIS) vehicles have better handing stability and path tracking performance. In view of this, a novel 4WIS electric vehicle (EV) with steer-by-wire (SBW) system is proposed in this paper. As to the 4WIS EV, a linear quadratic regulator (LQR) optimal controller is designed to make the vehicle track the desired path based on the linear dynamic model. Taking the effect of uncertainties in vehicle parameters into consideration, a robust controller utilizing μ synthesis approach is designed and the controller order reduction is implemented based on Hankel-Norm approximation. In order to evaluate the performance of the designed controllers, numerical simulations of two maneuvers are carried out using the nonlinear vehicle model in MATLAB/Simulink. Simulation results show that the robust controller is superior to the LQR optimal controller in tracking accuracy in terms of the nominal vehicle model. Furthermore, the robust controller can make the vehicle track the desired path well under the circumstances of different vehicle velocities and road friction coefficients, which indicates the robust controller has strong robust stability and good robust performance against parametric perturbations.