Steer-by-Wire (SbW) system is an advanced steering system where the conventional mechanical linkages between the steering wheel and the front wheels are removed, and replaced by electric actuators. Due to no direct mechanical linkages, accurately controlling the front wheels to track the movement of the steering wheel is becoming critical for the steering system performance. To reduce the effects caused by the nonlinear friction torque and alignment torque to the tracking performance of the SbW system, a Takagi-Sugeno (T-S) model is proposed to describe the nonlinear dynamics of the SbW system in this paper first. A fuzzy tracking controller is then designed to track the reference signal, and the H∞ tracking performance is guaranteed for a prescribed level under external disturbance and reference signal. The linear matrix inequality convex programming technique is used to obtain the fuzzy controller with the guaranteed H∞ tracking performance. The simulation results are presented in support of the performance and effectiveness of the proposed control scheme.