This paper develops LongNav-R1, an end-to-end multi-turn reinforcement learning (RL) framework designed to optimize Visual-Language-Action (VLA) models for long-horizon navigation. Unlike existing single-turn paradigm, LongNav-R1 reformulates the navigation decision process as a continuous multi-turn conversation between the VLA policy and the embodied environment. This multi-turn RL framework offers two distinct advantages: i) it enables the agent to reason about the causal effects of historical interactions and sequential future outcomes; and ii) it allows the model to learn directly from online interactions, fostering diverse trajectory generation and avoiding the behavioral rigidity often imposed by human demonstrations. Furthermore, we introduce Horizon-Adaptive Policy Optimization. This mechanism explicitly accounts for varying horizon lengths during advantage estimation, facilitating accurate temporal credit assignment over extended sequences. Consequently, the agent develops diverse navigation behaviors and resists collapse during long-horizon tasks. Experiments on object navigation benchmarks validate the framework's efficacy: With 4,000 rollout trajectories, LongNav-R1 boosts the Qwen3-VL-2B success rate from 64.3% to 73.0%. These results demonstrate superior sample efficiency and significantly outperform state-of-the-art methods. The model's generalizability and robustness are further validated by its zero-shot performance in long-horizon real-world navigation settings. All source code will be open-sourced upon publication.