This paper presents an accurate and fast 3D global localization method, 3D-BBS, that extends the existing branch-and-bound (BnB)-based 2D scan matching (BBS) algorithm. To reduce memory consumption, we utilize a sparse hash table for storing hierarchical 3D voxel maps. To improve the processing cost of BBS in 3D space, we propose an efficient roto-translational space branching and best-first search strategy. Furthermore, we devise a batched BnB algorithm to fully leverage GPU parallel processing. Through experiments in simulated and real environments, we demonstrated that the 3D-BBS enabled accurate global localization with only a 3D LiDAR scan and a 3D pre-built map. This method required only 878 msec on average to perform global localization and outperformed state-of-the-art feature-matching-based global localization methods in terms of accuracy and processing speed.