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In this paper, we propose an adaptive and dynamic scheduling method, called most fit task first (MFTF), for a class of computational grids, which are characterized by heterogeneous computing nodes and dynamic task arrivals. Some existing static scheduling methods assume that tasks arrive statically and may not perform well in the case of dynamic task arrivals. Our method can get stable task execution times whether tasks arrive statically or dynamically. We compare the task execution time with other methods to show the performance of the scheduling method.