In order to improve the dynamic performance of linear servo system and overcome the time varying problem of linear synchronous motor parameters, a model reference adaptive speed controller is designed. The inner loop of the system is a speed tracking controller based on the reference model. The outer loop adaptive mechanism adjusts the adjustable parameters of the speed tracking controller online and makes the generalized speed error between the output speed of the reference model and that of the control object approach zero. The design method of model reference adaptive speed controller based on Lyapunov stability theory is adopted. The generalized speed tracking error converges to zero, and the model reference adaptive speed control system has stability and convergence. Using Euler numerical integration method, the output speed curves of the reference model and the control object and the time domain response curve of the primary quadrature current state variable are obtained through computer numerical simulation. The global convergence of the adaptive speed control system is verified.