This study addresses the trajectory tracking problem for tail-sitter vertical takeoff and landing (VTOL) unmanned aerial vehicles (UAVs) across their entire flight envelope. We propose a trajectory tracking controller based on nonlinear model predictive control (NMPC) integrated with a neural network aerodynamic predictive model. The aerodynamic model of our designed NMPC reserves only a single nonlinear aerodynamic coefficient, reducing optimization complexity. The identification process for the neural network aerodynamic model involves two key steps: First, an aerodynamic model-free NMPC is employed to track a predefined circular ref-erence trajectory while maintaining coordinated flight, during which flight data is collected to train the neural network aerodynamic model. Subsequently, a Pareto-optimal set of models is selected based on two critical metrics—prediction accuracy and computational complexity—for trajectory tracking and evaluation. Simulation results demonstrate that compared with other parametric models, the proposed neural network aerodynamic NMPC effectively tracks the reference trajectory, significantly improving tracking accuracy while maintaining real-time computational performance, making it a promising candidate for real-world deployment.