This paper proposes a hybrid terminal sliding-mode observer based on the nonsingular terminal sliding-mode (NTSM) and the high-order sliding-mode (HOSM) for the rotor position and speed estimation in the permanent-magnet synchronous motor control system. An NTSM manifold is utilized to realize both fast convergence and better tracking precision. In addition, a derivative estimator is used to obtain the derivative of the sliding-mode function. Meanwhile, an HOSM control law is designed to guarantee the stability of the observer and eliminate the chattering, so that smooth back-electromotive-force (EMF) signals can be obtained without a low-pass filter. According to the back-EMF equations, the rotor position and speed of the motor can be calculated. Simulation and experimental results are presented to validate the proposed method.