This article investigates a fixed-time nonsingular terminal sliding mode control (FNTSMC) method with disturbance observer (DO). Using the vehicle's acceleration information, a fixed-time DO is designed to estimate the external uncertain disturbance of the system. Considering the nonzero initial error, a modified constant time headway strategy is proposed to overcome the influence of the nonzero initial error on the vehicle controller. In addition, a new terminal sliding mode control method is introduced to avoid the nonsingular problem and ensure that the vehicle spacing error converges in a fixed time. Finally, a numerical simulation is presented to show the proposed method's effectiveness.