In the sensorless control of brushless direct current motor (BLDCM), according to the chattering problems of traditional sliding mode observers, a novel non-singular terminal sliding mode observer (NTSMO) is proposed to estimate line back electromotive force. The designed non-singular terminal sliding mode surface can realize fast convergence in finite-time, and a novel sliding mode reaching law is introduced to weaken chattering. The estimation accuracy of back electromotive force is improved, the fast speed observation and control are realized. Finally, the stability of the observer is proved based on the Lyapunov function. The simulation results show that, compared with the traditional method, the proposed NTSMO can effectively suppress chattering and has a good speed estimation accuracy.