Multi-class classification models are often applied in real applications with multiple classes involved, such as credit card client analysis and disease diagnosis prediction. In fact, a network can be attacked by multiple hackers, which is also a typical multiple classes problem. Instead of building a firewall to prevent the network system, which is called a passive protection, one should find out the different attacking behaviors of the hackers for a positive defense. This paper promotes multi-criteria mathematical programming (MCMP) model for dealing with various kinds of attacks in network security. Without directly solving a convex mathematical programming problem, the proposed method only performs matrix computation for its optimal solution, which is easy to be realized. In addition, the concept of e-support vector is employed to facilitate the computation of large-scale applications. For nonlinear case, kernel technique is also applied. Using a newly well-known network intrusion dataset, called NSL-KDD, the paper demonstrates that the proposed method can achieve both high classification accuracies and low false alarm rates for multi-class network intrusion classification.