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Diagnosing acute leukemia is the necessary prerequisite to treating it. Multi-classification on the gene expression data of acute leukemia is help for diagnosing it which contains B-cell acute lymphoblastic leukemia (BALL), T-cell acute lymphoblastic leukemia (TALL) and acute myeloid leukemia (AML). However, selecting cancer-causing genes is a challenging problem in performing multi-classification. In this paper, weighted gene co-expression networks are employed to divide the genes into groups. Based on the dividing groups, a new regularized multinomial regression with overlapping group lasso penalty (MROGL) has been presented to simultaneously perform multi-classification and select gene groups. By implementing this method on three-class acute leukemia data, the grouped genes which work synergistically are identified, and the overlapped genes shared by different groups are also highlighted. Moreover, MROGL outperforms other five methods on multi-classification accuracy. [ABSTRACT FROM AUTHOR]