The ground taxiing phase is a crucial stage for the autonomous takeoff and landing of fixed-wing unmanned aerial vehicles (UAVs), and its trajectory tracking accuracy and stability directly determine the success of the UAV’s autonomous takeoff and landing. Therefore, researching the adaptive robust optimal control technology for UAV taxiing is of great significance for enhancing the autonomy and environmental adaptability of UAVs. This study integrates the linear quadratic regulator (LQR) with sliding mode control (SMC). A compensation control signal is generated by the SMC to mitigate the potential effects of uncertain parameters and random external disturbances, which is then added onto the LQR output to achieve a robust optimal controller. On this basis, through ANFIS (Adaptive Neuro-Fuzzy Inference System), the nonlinear mapping relationship between multiple state parameters such as speed, lateral/heading deviation and the weight matrix of the LQR controller is learned, realizing a data-driven adaptive adjustment mechanism for controller parameters to improve the tracking accuracy and anti-interference stability of the UAV’s taxiing trajectory.