This paper proposed a sensorless speed control strategy of a permanent-magnet synchronous motor (PMSM) using a full-order terminal sliding-mode observer (FOTSMO) with the stator resistance estimated. In the proposed observer, the low pass filter (LPF) in the conventional sliding-mode observer (SMO) is removed, so the control strategy can overcome the time delay and weaken the chattering phenomenon. Meanwhile, the time-varying stator resistance is identified online to improve the steady-state performance of the observer. The stator resistance adaptive law is determined by the Lyapunov second method, and the stability of the FOTSMO is proved. the feasibility of the proposed method is verified by simulations and experiments.