This paper proposes a new approach for gene expression classification by using a multi-class support vector machine (SVM) with feature selection. The proposed algorithm is based on the One-Versus-All (OVA) multi-class strategy, which learns binary 1-norm SVM models. As the 1-norm SVM solution is very sparse, the algorithm can automatically suppress a large number of dimensions that correspond to null weights. This feature elimination improves the classification results for high-dimensional gene expression datasets. Empirical test results on 25 gene expression datasets show that our multi-class SVM eliminates 99% of full dimensions, resulting in 7.1%, 4.03% increase in accuracy compared to training SVM, random forest models on the full dimensions of gene expression datasets, respectively.