This paper proposes VLA-AN, an efficient and onboard Vision-Language-Action (VLA) framework dedicated to autonomous drone navigation in complex environments. VLA-AN addresses four major limitations of existing large aerial navigation models: the data domain gap, insufficient temporal navigation with reasoning, safety issues with generative action policies, and onboard deployment constraints. First, we construct a high-fidelity dataset utilizing 3D Gaussian Splatting (3D-GS) to effectively bridge the domain gap. Second, we introduce a progressive three-stage training framework that sequentially reinforces scene comprehension, core flight skills, and complex navigation capabilities. Third, we design a lightweight, real-time action module coupled with geometric safety correction. This module ensures fast, collision-free, and stable command generation, mitigating the safety risks inherent in stochastic generative policies. Finally, through deep optimization of the onboard deployment pipeline, VLA-AN achieves a robust real-time 8.3x improvement in inference throughput on resource-constrained UAVs. Extensive experiments demonstrate that VLA-AN significantly improves spatial grounding, scene reasoning, and long-horizon navigation, achieving a maximum single-task success rate of 98.1%, and providing an efficient, practical solution for realizing full-chain closed-loop autonomy in lightweight aerial robots.