Microarray gene expression profile data is used to accurately predict different tumor types, which has great value in providing better treatment and toxicity minimization on the patients. However, it is difficult to classify different tumor types using microarray data because the number of samples is much smaller than the number of genes. It has been proved that a small feature gene subset can improve classification accuracy, so feature gene selection and extraction algorithm is very important in tumor classification. In this paper, a novel hybrid gene selection method is proposed to find a feature gene subset so that the feature genes related to certain cancer can be kept and the redundant genes can be leave out. In the proposed method, we combine the advantages of the PCA and the LDA and proposed a novel feature gene extraction scheme. We also compared several kinds of parametric and non-parametric feature gene selection methods. We use the SVM as the classifier in the experiment and compare the performance of three common SVM kernels. Their differences are analyzed. Using the n-fold cross validation, the proposed algorithm is carried out on three published benchmark tumor datasets and experimental results show that this algorithm leads to better classification performance than other methods.