This paper studies global nonsingular fixed-time terminal sliding mode control (GNFTSMC) for a second-order uncertain permanent magnet synchronous motor (PMSM) system to further improve its speed tracking performance. The newly proposed GNFTSMC consists of a time-dependent terminal sliding surface and a piecewise continuous sliding mode control law. By a time-dependent function constructed from the initial conditions of the system and a predefined time, the sliding surface is always reached at the initial instant and forced to a traditional fast terminal sliding surface after the predefined time. Based on Filippov's stability principles, the globally fixed-time stability of the GNFTSMC is proved. Furthermore, a priori time independent of the initial conditions is derived to estimate the boundary of the settling time of the closed control loop. Then, the control law is analyzed to be always nonsingular. Thus, the GNFTSMC-based speed controller for the PMSM speed tracking system is developed. Finally, simulations are conducted for the proposed controller and other terminal sliding mode controllers. The results show that compared to the other controllers, the PMSM system based on GNFTSMC displays improved performance characteristics of faster speed response, smaller chattering and higher current efficiency.