To solve the problem of finite-time constraints when the missile intercepts a maneuvering target in the terminal guidance stage, the mathematical model of the target interception system is established considering the dynamic delay of the autopilot.To solve the problem of poor guidance stability caused by the singularity of the traditional terminal sliding mode guidance law, a new non-singular terminal sliding mode guidance law based on the improved Extended State Observer (ESO) is proposed.This method ensures that the Line-of-Sight (LOS) angular rate converges to zero in a finite time and converges quickly at the equilibrium point.In order to avoid curve chatter caused by the traditional ESO, an improved ESO is adopted to accurately estimate external disturbances and compensate for the systems state.A model of the surface-to-air missile is designed for simulation verification.The simulation results show that this method not only shortens the systems convergence, but also improves the guidance precision of the surface-to-air missile.