The continuous time mathematical model of electrically excited linear synchronous motor is established, which is suitable for the design of speed controller. A singleinputsingleoutput transfer function between the primary quadrature axis voltage and the primary mechanical speed is established with reasonable assumptions. An adaptive speed controller is designed by using local parameter optimization gradient method, which consists of only one integrator, one multiplier and two proportional elements. The adaptive speed controller without the traditional current loop accelerates the response speed and simplifies the system structure. The controller designed by MATLAB numerical simulation software is used to analyze the influence of the factors such as the adaptive gain adjustment coefficient and the generalized error feedback coefficient on the stability and convergence of the adaptive speed control system. Simulation results show the effectiveness of the adaptive speed control strategy.