This paper presents a case study to effectively run a parallel branch and bound application on the Grid. The application discussed in this paper is a fine-grain application and is parallelized with the hierarchical master-worker paradigm. This 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. This hierarchical manner reduces communication overhead by localizing frequent communication in tightly coupled computing resources, or a single PC cluster. The algorithm is implemented on a Grid testbed by using GridRPC middleware, Ninf-G and Ninf. In the implementation, communication among PC clusters is securely performed via Ninf-G, which uses Grid security service on the Globus Toolkit, and communication among computing nodes in each PC cluster is performed via Ninf, which enables fast invocation of remote computing routines. The experimental results showed that implementation of the application with the hierarchical master-worker paradigm using a combination of Ninf-G and Ninf effectively utilized computing resources on the Grid testbed in order to run the fine-grain application, where the average computation time of the single task was less than 1[sec].