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Resource management and task scheduling are very important and complex problems in grid computing environment. It is necessary to do resource state prediction to get proper task scheduling. Ant algorithm is a new heuristic algorithm. The inherent parallelism and scalability make the algorithm very suitable to be used in grid computing task scheduling whose structure is dynamic changed almost all the time. In this paper, we validate the scalability of ant algorithm, propose a simple grid simulation architecture for resource management and task scheduling, and design an ant algorithm for grid task scheduling. We put the algorithm into the simulation architecture, and get good results in respond time, resource average utilization, and task fulfill proportion.