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Tasks' smallest completion time is a fundamental goal of the grid scheduling, however, the completion time of tasks and cost are often anti-correlated. In this paper, A budget constrained optimal time scheduling on the grid computing platforms is discussed, where resources have different speeds of computation and prices. The task scheduling problem is converted into a linear programming problem. Each resource gains the optimal execution time and the smallest completion time of the task were obtained, under the condition of the budget constraint, using of the simplex algorithm to obtain the optimal solution. The simulation results show that the performance of the algorithm is superior to other similar algorithms.