The purpose of this paper is to introduce new approaches for kernel logistic regression (KLR) in a semi-supervised setting. Using the special structure of Laplacian kernel matrices, we propose new formulations which minimize the negative log likelihood of the KLR model efficiently. Also, we propose new algorithms for pool-based active learning based on A-optimality in which the semi-supervised KLR is used to estimate the class probabilities. We show that the active learning algorithms can be carried out in the fea- ture space defined by the associated kernel matrices. We give experimental results showing that the proposed active learning method generate accurate classifiers using a fewer number of labeled data points compared with the random queries.