This paper proposes an adaptive neural network (ANN) and nonlinear dynamic inversion (NDI) based controller for large-angle maneuver attitude control problems in quadrotor UAVs, which aims to overcome the challenges posed by model uncertainty and external disruptions on control effectiveness. The NDI serves as the primary controller, while the ANN acts as the compensation controller. Firstly, the attitude dynamic model of the quadrotor UAV is presented in the paper. Then, a control method based on dynamic inversion theory is developed to achieve large-angle maneuver control for the quadrotor UAV, which takes into account the coupling and nonlinearity of the attitude dynamic model. Additionally, in order to address inaccuracies caused by model uncertainty and unidentified external disruptions, compensation control signals are evaluated and generated by using an adaptive neural network. The update rate of neural network weights is designed using Lyapunov theory to achieve online adaptive control. Ultimately, to evaluate the effectiveness of the proposed control method, numerical simulations are conducted. According to the numerical simulation results, the proposed controller exhibits superior performance compared to traditional controllers in terms of both robustness and attitude tracking accuracy.