The design problem of the terminal guidance law for intercepting high-speed maneuvering target considering the second-order dynamic characteristics of the autopilot was discussed.A local stability theory was proposed and was used in analysis of the system state variables.According to the influence of variables on the guidance effect the system was divided into two subsystems.Then we designed the Lyapunov function for the subsystems and proved their stabilities and launched the global stability from the local stability.Throughout the whole design process only the change of line-of-sight rate was taken into consideration which simplified the design process greatly.The design of the guidance law could effectively overcome the impact of the autopilot dynamic delay on guidance accuracy.The simulation results show that when the target is making maneuver and there is a large lag in the autopilot the guidance law still has a high guidance precision.