The steer-by-wire (SbW) system, in which the conventional mechanical linkage between the steering wheel and the front wheel is removed, is capable of acting as an actuator for the active front steering system enhancing vehicle handling performance and safety. Several control strategies have been utilized to control the front wheel subsystem, which is the main part of the SbW system, and the steering response of SbW in the presence of system uncertainties and external disturbance has been improved; however, improvement of the controller transient response is not considered in most of these control strategies. In this paper a nonsingular fast terminal sliding mode (NFTSM) control method for the front wheel subsystem is first established. The NFTSM technique aims to provide a fast transient response for the front wheel tracking controller in the existence of system uncertainties and disturbance including the tire self-aligning torque, Coulomb friction torque and variation of road condition. Simulation results confirm that the proposed nonsingular fast terminal sliding mode controller not only has strong robustness against uncertainties but also improves the transient response of the tracking controller.