In view of the development prospect of vehicle steer-by-wire (SbW) technology, this paper proposes a recursive terminal sliding mode (RTSM) control scheme for an SbW system. Firstly, we describe the SbW system by a second-order dynamic model, where the control input is the voltage of steering motor and the system output is the steering angle of front wheels. For simplicity, the self-alignment torque and friction generated by tire-road contact are considered as external disturbances. Secondly, an RTSM controller is designed for the SbW system, which can not only deal with the parametric uncertainties, but also effectively estimate the self-alignment torque coefficient. In addition, we prove the stability of RTSM control system from the perspective of Lyapunov, and give suitable control parameters under stable conditions. Finally, the steering control is simulated along a slalom path and a circular path, respectively. Simulation results show that, compared with conventional sliding mode (CSM) control, the proposed RTSM control strategy possesses obvious advantages in terms of higher tracking accuracy, faster response speed and firmer robustness.