Neural implicit representations have recently demonstrated considerable potential in the field of visual simultaneous localization and mapping (SLAM). This is due to their inherent advantages, including low storage overhead and representation continuity. However, these methods necessitate the size of the scene as input, which is impractical for unknown scenes. Consequently, we propose NeB-SLAM, a neural block-based scalable RGB-D SLAM for unknown scenes. Specifically, we first propose a divide-and-conquer mapping strategy that represents the entire unknown scene as a set of sub-maps. These sub-maps are a set of neural blocks of fixed size. Then, we introduce an adaptive map growth strategy to achieve adaptive allocation of neural blocks during camera tracking and gradually cover the whole unknown scene. Finally, extensive evaluations on various datasets demonstrate that our method is competitive in both mapping and tracking when targeting unknown environments.