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According to the dependence and deadline of the grid workflow tasks, the effective degrees and MIPS of the grid resources, a new algorithm called the priority tasks scheduling algorithm based on the grid resource prediction is presented. The algorithm uses DAG to find the critical path, obtain the deadline of every task and compute their PRI (priority). The algorithm takes the below problems into consideration: the request of user, the type of resources and re-scheduling of failed tasks. The result shows that the algorithm is effective.