It is important in bioinformatics research and applications to select or discover informative genes of a tumor from microarray data. However, most of the existing methods are based on models which assume that the gene expressions are normal distributed, which is often violated in practice. In this paper, we propose an information criterion for informative gene selection by ranking the genes with the Kullback-Leiber discrimination information of two probability distributions of the expression levels on the tumor and normal (or another type of tumor) samples. We use support vector machine (SVM) to construct the tumor diagnosis system using certain top informative genes. The experiments on two well-known data sets (colon data and leukemia data) show that the information criterion can make the tumor diagnosis system reach 94.4% and 100% correctness rate of diagnosis on these two datasets, respectively.