When considering the robust control of fixed-wing Unmanned Aerial Vehicles (UAVs), a conflict often arises between addressing nonlinearity and meeting fast-solving requirements. In existing studies, the less nonlinear robust control methods have shown significant improvements that parallel computing and dimensionality reduction techniques in real-time applications. In this paper, a nonlinear fast Tube-based Robust Compensation Control (TRCC) for fixed-wing UAVs is proposed to satisfy robustness and fast-solving requirements. Firstly, a solving method for discrete trajectory tubes was proposed to facilitate fast parallel computation. Subsequently, a TRCC algorithm was developed that minimized the trajectory tube to enhance robustness. Additionally, considering the characteristics of fixed-wing UAVs, dimensionality reduction techniques such as decoupling and stepwise approaches are proposed, and a fast TRCC algorithm that incorporates the control reuse method is presented. Finally, simulations verify that the proposed fast TRCC effectively enhances the robustness of UAVs during tracking tasks while satisfying the requirements for fast solving.