Relevant gene selection is crucial for analyzing cancer gene expression datasets including two types of tumors in cancer classification. Intrinsic interactions among selected genes cannot be fully identified by most existing gene selection methods. In this paper, we propose a weighted general group lasso (WGGL) model to select cancer genes in groups. A gene grouping heuristic method is presented based on weighted gene co-expression network analysis. To determine the importance of genes and groups, a method for calculating gene and group weights is presented in terms of joint mutual information. To implement the complex calculation process of WGGL, a gene selection algorithm is developed. Experimental results on both random and three cancer gene expression datasets demonstrate that the proposed model achieves better classification performance than two existing state-of-the-art gene selection methods.