In this paper, we present a resource broker architecture for a computational Grid which uses Genetic Algorithm (GA) for brokering. Resource brokering implies selection of appropriate resource providers for jobs submitted to the Grid. Resource brokering is normally done with the objective of optimizing some performance parameter such as minimizing the total cost of running the jobs or maximizing the utilization of Grid resources. It is a challenging task since the search space for the problem consists of all possible allocations of submitted jobs to available resource providers in a Grid and may be very large. GAs are found to be efficient for such optimization problems. Moreover, the configuration and workload of a Grid is dynamic in nature. Our GA based resource broker tries to address these issues so that jobs are scheduled efficiently.