This paper focuses on semi-supervised classification problem by using Transductive Support Vector Machine. Traditional TSVM for semi-supervised classification firstly train an SVM model with labeled data. Then use the model to predict unlabeled data and optimize unlabeled data prediction to retrain the SVM. TSVM always uses a predefined kernel and fixed parameters during the optimization procedure and they also suffers potential over-fitting problem. In this paper we introduce proposed quasi-linear kernel to the TSVM. An SVM with quasi-linear kernel realizes an approximate nonlinear separation boundary by multi-local linear boundaries with interpolation. By applying quasi-linear kernel to semi-supervised classification it can avoid potential over-fitting and provide more accurate unlabeled data prediction. After unlabeled data prediction optimization, the quasi-linear kernel can be further adjusted considering the potential boundary data distribution as prior knowledge. We also introduce a minimal set method for optimizing unlabeled data prediction. The minimal set method follows the clustering assumption of semi-supervised learning. The pairwise label switching is allowed between minimal sets. It can speed up optimization procedure and reduce influence from label constrain in TSVM. Experiment results on benchmark gene datasets show that the proposed method is effective and improves classification performances.