In this paper, we address the issues of resource management and fault tolerance in Grids. In Grids, the state of the selected resources for job execution is a primary factor that determines the computing performance. Specifically, we propose a resource manager for optimal resource selection. The resource manager automatically selects the optimal resources among candidate resources using a genetic algorithm. Typically, the probability of failure is higher in Grid computing than in a traditional parallel computing and the failure of resources affects job execution fatally. Therefore, a fault tolerance service is essential in computational Grids and Grid services are often expected to meet some minimum levels of quality of service (QoS) for desirable operation. To address this issue, we also propose fault tolerance service to satisfy QoS requirements. We extend the definition of failures, such as process failure, processor failure, and network failure, and design the fault detector and fault manager. The simulation results indicate that our approaches are promising in that (1) our resource manager finds the optimal set of resources that guarantees the optimal performance; (2) the fault detector detects the occurrence of resource failures; and (3) the fault manager guarantees that the submitted jobs complete and improves the performance of job execution due to job migration even if some failures happen.