Abstract: A new class-Weighted Dual v-SVM, termed as WD v-SVM, is proposed and Karush-Kuhn Tucker condition (KKT) is derived for it. The dual parameters v+ and v- are analyzed theoretically, and it is deduced that they represent the upper and the lower bound for the percentage of bounded support vectors and the support vectors in the weighted positive or negative class respectively, which is similar to their counterparts in v-SVM. Therefore, the classification performance of small sample class is improved through adjusting its class weight. Experimental results show that the WD v-SVM not only keeps the advantages of v-SVM, but also solves the problem of larger classification error rate of small sample class.