Grid computing promises the ability to share geographically and organizationally distributed resources to increase effective computational power and resource utilization. However, for the Grid computing to be successful, it is very important to provide middleware services that assist Grid users to easily interact with Grid environments. In this paper, we have designed and implemented a new general-purpose OGSI-compliant Grid resource broker service to hide the underlying complexity of the Grid resources from Grid users and to meet not only Grid user requirements but also resource owner policies. It focuses on discovering and scheduling dynamic resources scattered across multiple organizations. Furthermore, it can be integrated with various scheduling services. We also present experimental results and demonstrate the effectiveness of our Grid broker service.