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Grid computing has recently seen a great importance in diverse applications domains of scientific, industrial, and commercial activities, which demand huge computational power. Unlike traditional cluster computing, large scale grids permit the sharing of grid resources spread through different administrative sites autonomy. The distributed and dynamic features of grid resources, their architectures heterogeneity, and unreliable interconnection network increases the probability of attacks and malicious behavior of grid resources. In Grid applications, reliability and security assurance of execution are two basic requirements. Thus, it is necessary to guarantee that, among the shared grid resources, there are no malicious behaviors interested in invalidating or corrupting the job results. In order to ensure reliable and safe jobs computation in grid systems, we have proposed a new approach for tolerating malicious grid resources by using reputation to improve the efficiency of majority voting mechanisms. The grid broker service investigates the trustworthy of the grid resources that are used in the voting procedure; this investigation is based on reputation management system which maintains a reputation value for each grid resource based on its historical behavior. The validation of the result is then decided based on the reputation level of the grid resources.