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Grid computing is a group of clusters connected over high-speed networks that involves coordinating and sharing computational power, resource utilization is an important issue. That's why some new technique needed to maximize Grid resource utilization. This paper proposes grid level resource scheduling with Job Grouping strategy that maximizes the resource utilization and minimizes processing time of jobs. Also Best Fit followed by Round Robin policy applies at local level to achieve better performance. This method avoids starvation problem of jobs.