The incorporation of prior knowledge into SVMs for classification is the key element that allows increasing the performance to many applications. Wu proposed weighted margin support vector machine (WMSVM), the scalability aspect of the approach to handle large data sets still needs much of exploration. In this paper, we describe a generalization of Weighted Margin Multi-class Core Vector Machine (WMMCVM) which views the Weighted Margin Multi-class SVM as a Center-Constrained MEB Problem, so the QP problem is then solved using the CVM technique to achieve scalability to handle large data sets. Experimental results indicate that the proposed WMMCVM technique gives a better performance than the original one.