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Grid computing is a new model that uses a network of processors connected together to perform bulk operations allows computations. Since it is possible to run multiple applications simultaneously may require multiple resources but often do not have the resources; so there is a scheduling system to allocate resources is essential. In view of the extent and distribution of resources in the grid computing, task scheduling is one of the major challenges in grid environment. Scheduling algorithms must be designed according to the current challenges in grid environment and they assign tasks to resource to decrease makespan which is generated. Because of the complex issues of scheduling tasks on the grid is deterministic algorithms work best for this offer. In this Paper, the Queen-bee algorithm is presented to solve the problem and the results have been compared to several other meta-heuristic algorithms. Also, it is shown that the proposed algorithm decline calculation time beside decreasing makespan compared to other algorithms. Keyword: Grid computin