This paper proposes a parallel branch and bound algorithm that efficiently runs on the Grid. The proposed algorithm is parallelized with the hierarchical master-worker paradigm in order to efficiently compute fine-grain tasks on the Grid. The hierarchical algorithm performs master-worker computing in two levels, computing among PC clusters on the Grid and that among computing nodes in each PC cluster, and reduces communication overhead by localizing frequent communication in tightly coupled computing resources, or a PC cluster. On each PC cluster, granularity of tasks dispatched to computing nodes is adaptively adjusted to obtain the best performance. The algorithm is implemented on the Grid testbed by using GridRPC middleware, Ninf-G and Ninf. In the implementation, communication among PC clusters is securely performed via Ninf-G using the Grid Security Infrastructure, and fast communication in each PC cluster is performed via Ninf. The experimental results showed that parallelization with the hierarchical master-worker paradigm using combination of Ninf-G and Ninf effectively utilized computing resources on the Grid in order to run a fine-grain application. The results also showed that the adaptive task granularity control automatically gave the same or better performance compared to performance with manual control.