The brushless DC motor (BLDCM) has many advantages. As a result, it is widely used in electric vehicle (EV) drive systems. To improve the reliability of the motor control system, a position sensorless control strategy based on a sliding mode observer (SMO) is proposed. The global fast terminal sliding mode observer (GFTSMO) is proposed to enhance the control performance of the SMO control system. The advantages of the linear sliding mode and the nonsingular terminal sliding mode (NTSM) are combined in the control strategy. The convergence speed of the system state is enhanced. The motor commutation point is obtained with the observation of the back EMF, and the instantaneous torque value of the motor is calculated. Therefore, the position sensorless control of the BLDCM is realized. Experimental results show that the proposed control strategy can improve the convergence speed, dynamic characteristics and robustness of the system.