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Grid computing provides a platform for users to access worldwide distributed resources. To meet the timing constrains and quality requirements imposed by the tasks running on a grid, the resources assigned to the tasks may need to be periodically reallocated. Thus, an effective strategy for reinforcing resources to or reclaiming resources from the tasks is needed. In this paper, a novel scheduling algorithm is proposed for grid computing with periodical resource reallocation. It migrates the ongoing tasks from a set of computing nodes to another set so as to fully employ the newly available computing power. To achieve high performance computing, the algorithm also balances the workload of the grid in the meanwhile of task migration. In this paper, the simulation results show the usefulness and effectiveness of our scheduling algorithm.