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Grid systems tend to grow in size, but currently deployed state-of-the-art schedulers have inherent scalability limits due to centralization. In this paper, we present a novel, fully decentralized scheduling approach for Grid Computing. The approach is inspired from the gravitational field in physics. In the approach, a task autonomously selects a suitable computing node based on local information without dedicated servers or coordinators. An important feature of the approach is that it schedules compute-intensive tasks so that the workload of Grid systems achieves balanced as soon as possible. From simulation results, the approach can scale to a large number of nodes and has a fast task convergence rate, maintaining high Grid utilization and good capability of balanced workload.