Gene selection is applied to reduce the number of genes in many applications where gene expression has a high dimension. Existing gene selection methods focus on finding relevant genes, but they often ignore the redundancy among the genes. A novel framework is presented which integrates the removal of feature irrelevance and detection of feature redundancy. The proposed framework firstly removes the irrelevant genes based on the popular gene selection methods (e.g., information gain). And a sparse representation model is designed for the left genes, which aims at removing the redundant genes. Finally cancer prediction is done based on the selected gene space with the classification algorithms. A series of experiments on real data sets have shown that the proposed framework outperforms the existing typical gene selection methods.