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In the grid systems, scheduling is a major issue in their operation, which is also an important problem in other area such as manufacturing, process control, economics, operation research and, etc. One motivation of grid computing is to aggregate the power of widely distributed resources, and provi.de non-trivial services to users. To achieve this goal, an efficient grid scheduling system is an essential part of the grid.This paper presents and evaluates a new method for task scheduling in grid computing systems to minimize its execution time. With regard to that this problem is a NP-Hard problem; so the evolutionary algorithms are the best choice for solving this problem. In this paper, contrary to prior ways, the new string representation and crossover operator has been used, communication costs hasn't been ignored and presents as a major factor for reaching to optimum solution.