This article presents a novel neural network-based hybrid mode-switching control strategy, which successfully stabilizes the flapping wing aerial vehicle (FWAV) to the desired 3-D position. First, a novel description for the dynamics, resolved in the proposed vertical frame, is proposed to facilitate further position loop controller design. Then, a radial base function neural network (RBFNN)-based adaptive control strategy is proposed, which employs a switching strategy to keep the system away from dangerous flight conditions and achieve efficient flight. The learning process of the neural network pauses, resumes, or alternates its update strategy when switching between different modes. Moreover, saturation functions and barrier Lyapunov functions (BLFs) are introduced to constrain the lateral velocity within proper ranges. The closed-loop system is theoretically guaranteed to be semiglobally uniformly ultimately bounded with arbitrarily small bound, based on Lyapunov techniques and hybrid system analysis. Finally, experimental results demonstrate the excellent reliability and efficiency of the proposed controller. Compared to existing works, the innovations are the put forward of the vertical frame and the cooperative switching learning and control strategies.