The existing prescribed performance control (PPC) strategies exhibit fragility and non-guarantee of prescribed performance when they are applied to dynamic systems with actuator saturation, and moreover, all of them are unable to quantitatively design prescribed performance. This article aims at remedying those deficiencies by proposing a new non-fragile PPC method for waverider vehicles (WVs) such that quantitative prescribed performance can be guaranteed for tracking errors in the presence of actuator saturation. Firstly, readjusting performance functions are developed to achieve quantitative prescribed performance and prevent the fragile problem. Then, low-complexity fuzzy neural control protocols are presented for velocity subsystem and altitude subsystem of WVs, while there is no need of recursive back-stepping design. Furthermore, auxiliary systems are designed to generate effective compensations on control constraints, which contributes to the guarantee of desired prescribed performance, being proved via Lyapunov synthese. Finally, compared simulation results are given to validate the superiority.