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Grid computing is a high performance computing environment to solve larger scale computational demands. Grid computing contains resource management, task scheduling, security problems, information management and so on. Task scheduling in an important aspect of distributed computing. As grid computing is a form of distributed computing with heterogeneous resources working in a shared environment with no central control. The main aim of Grid scheduling is to increase the system throughput and to satisfy the job requirements from the available resources. This work proposes a resource requirement (R2) prioritized task-scheduling algorithm for grid computing. This algorithm is based on prioritizing the resource requirement of the jobs which schedules the jobs taking into account the memory requirement of the jobs. It is named as the scheduling algorithm. It is compared with one of the widely used grid scheduling algorithm MinMin and has been tested in simulated grid environment. The experimental results showed a significant improvement of in terms of a makespan and system utilization.