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Grid Computing is a widespread distributed computing environment that consists of heterogeneous resources and it provides huge computational power for the large scale distributed application. In this job scheduling is an essential objective to prioritize the jobs based on the job characteristics. It is a big challenge to design and implement an efficient Job Scheduling algorithm and the Job Scheduling model. This paper proposes the priority based Job Scheduling algorithm with Nonpreemptive Priority (NPRP) Job Scheduling model. The priority based job scheduling algorithm is the combination of Backfill algorithm and Earliest Deadline based algorithm. The proposed model has been integrated with Care Resource Broker (CRB) which supports virtualized grid environment. The proposed model has been integrated with CRB helps to make the intelligent scheduling decisions for prioritizing the jobs and also the proposed model minimizes the turnaround time, waiting time and response time of the jobs available in the queue and the user's quality of service has been maximized in the heterogenous and virtualized grid environment.