Most semi-supervised learning models propagate the labels over the Laplacian graph, where the graph should be built beforehand. However, the computational cost of constructing the Laplacian graph matrix is very high. On the other hand, when we do classification, data points lying around the decision boundary (boundary points) are noisy for learning the correct classifier and deteriorate the classification performance. To address these two challenges, in this paper, we propose an adaptive semi-supervised learning model. Different from previous semi-supervised learning approaches, our new model needn't construct the graph Laplacian matrix. Thus, our method avoids the huge computational cost required by previous methods, and achieves a computational complexity linear to the number of data points. Therefore, our method is scalable to large-scale data. Moreover, the proposed model adaptively suppresses the weights of boundary points, such that our new model is robust to the boundary points. An efficient algorithm is derived to alternatively optimize the model parameter and class probability distribution of the unlabeled data, such that the induction of classifier and the transduction of labels are adaptively unified into one framework. Extensive experimental results on six real-world data sets show that the proposed semi-supervised learning model outperforms other related methods in most cases.