This study proposes a radial basis function neural network disturbance observer (RBFNNDO) based anti-saturation backstepping controller for hypersonic vehicles with input saturations and multiple disturbances. Firstly, in response to the problem of “exploding complexity” in backstepping controller, we adopted finite-time tracking differentiators (FTD), which realized higher tracking accuracy and tracking speed than those of the existing methods. Secondly, we developed multivariable neural network disturbance observers to estimate the lumped disturbances involving aerodynamic uncertainties and external disturbances, thereby improving the robustness of the proposed controller. Thirdly, in order to alleviate the input saturation and minimize the duration time, we used an adaptive fixed-time anti-saturation compensator (AFAC). The simulation results have proven that our proposed backstepping controller outperforms other existing methods in terms of control performance and saturation time.