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The cancer classification through gene expression patterns becomes one of the most promising applications of the microarray technology. It is also a significant procedure in bioinformatics. In this study a grid computing based evolutionary mining approach is proposed as discriminant function for gene selection and tumor classification. The proposed approach is based on the grid computing infrastructure for establishing the best attributes set. The discriminant analysis based on vector distant of median method as the evaluation function of genetic algorithm which lays stress on find the key attributes set of the data set to establish the best attributes set for constructing a classification response model with highest accuracy. We show experimentally that the proposed approach for several benchmarking cancer microarray data sets can work effectively and efficiently, and the results of the proposed methods are superior to or as well as other existing methods in literatures.