This paper presents a Transductive Support Vector Machine (TSVM) with quasi-linear kernel based on a clustering assumption for semi-supervised classification. Since the potential separating boundary is located in low density area between classes, a modified density clustering method by considering label information is firstly introduced to extract the information of potential separating boundary in low density region between different classes. Then the information is used to compose a quasi-linear kernel for the TSVM. The optimization of TSVM is further speeded up by developing a pairwise label switching method on minimal sets. Experiment results on benchmark datasets show that the proposed method is effective and improves classification performances.