Aiming at the problems that the sliding mode control permanent magnet linear synchronous motor (PMLSM) cannot achieve finite time control and the global sliding mode control (GSMC) cannot achieve rapid convergence, an improved GSMC algorithm is used to design the linear servo speed controller. The algorithm uses a dynamic sliding mode surface combined with a nonlinear term and a linear term and a constant velocity approaching law. The nonlinear sliding mode surface decay function is composed of three exponential function terms to form a first-order derivable function, and it can decay to zero in a finite time. The simulation results show that the improved GSMC not only makes the system globally robust, but also accelerates the response speed and improve anti-interference ability while ensuring high tracking accuracy.