Abstract: A prescribed performance control method was proposed for the hypersonic flight vehicle non-affine model. A new performance function was designed to ensure the transient performance and steady state performance of the controller. The initial constricted system was transformed into the equivalent unrestricted system by constructing the transformed error function to simplify controller design. The longitudinal dynamics model of the hypersonic flight vehicle was decomposed into velocity and altitude subsystems and the control laws were designed separately. For the altitude subsystem, a high-order tracking differentiator was used to estimate the error, and the fuzzy function was introduced to approximate the unknown, avoiding the repeated derivation in the back-stepping control. For the velocity subsystem, the proportional integral controller was directly designed according to the prescribed performance function. Finally, the effectiveness of the controller was verified by simulation experiments. Results show that, the designed control laws can improve the transient performance and steady-state accuracy under the condition of parameter uncertainty and disturbance, and reduce the computational load.