In order to solve the problem of stable trajectory control of hypersonic vehicle longitudinal motion model, a backstepping control method was designed to ensure the prescribed performance on the basis of non-affine model. For the velocity subsystem, the non-affine control law was directly designed to ensure the prescribed performance, and the altitude subsystem was transformed into a strict feedback form through reasonable transformation to facilitate the design of backstepping control steps. Based on dynamic performance and steady-state accuracy, the preset performance function was designed to limit the stability of tracking error within the preset range, and the instruction filter was introduced to effectively overcome the problem of repeated derivation of virtual signal in traditional inversion control. The design of the controller does not depend on the exact model. The radial basis function was introduced to approximate the unknown function in the process. As a result, the control law has satisfactory robustness and practicability. Based on the Lyapunov stability theory, the stability of all closed-loop systems was proved. Simulation results show that the controller can track the reference signal stably.