Next point-of-interest (POI) recommendation is a flourishing task within location-based services, where user check-in behaviors are influenced not only by their personal preferences and current intents but also by the intricate geographical dependencies among POIs. Existing methods generally construct pre-defined POI graphs and learn unified static representations. However, the pre-defined graphs heavily depend on domain knowledge and data quality. Few studies have explored the feasibility of adaptive graph learning to replace manually designed graphs, but they ignore the important dynamic dependencies among POIs in spatial-temporal scenarios. To tackle these challenges, we propose a novel framework Dynamic-aware Adaptive Graph Learning (DyAGL) for next POI recommendation. Specifically, to capture dynamic and intricate dependencies among POIs, we first design a spatial-temporal enhanced adaptive graph learning module, which mines fine-grained geographical dependencies automatically via similarity learning of POI embeddings. Moreover, we propose a dynamic personalized intent-aware module that incorporates the learned fine-grained representations of POIs and personalized spatial-temporal information to further capture user dynamic behavioral intents and preferences. Extensive experiments on three real-world public datasets demonstrate the superior performance of DyAGL.