In this paper, an Improved Nonsingular Terminal Sliding-mode (INTSM) observer is proposed to estimate the speed of the permanent magnet synchronous motor (PMSM). The Nonsingular Terminal Sliding-mode (NTSM) not only inherits the good performance to track the state error, but also has the characteristic of limited time convergence. However, the conventional NTSM control law is too complex to apply in practice. The INTSM takes the thoughts of the fast Terminal Sliding-mode and uses a new nonlinear term to replace the conventional term. As a result, the new observer owns the characteristics of global fast convergence and simple control law. At last, the proposed method proves to be effective through the theoretical analysis and simulation test.