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Grid computing is a newly developed technology. Although the developmental tools and techniques for the grid have been extensively studied, the reliability of grid service can not satisfy the real-world application requirements. To resolve this problem, this paper introduces a fault recovery mechanism into grid nodes and gives a constraint on recovery amount. Moreover, a multi-objective optimization model is presented to address the task scheduling problem and an ant colony optimization (ACO) is developed to solve the problem effectively. A numerical example is given to show the modeling procedures and efficiency of the ACO.