This paper analyzes the problem of sensitivity to noise in the mean square criterion of Gaussian- Laplacian regularized (GLR) algorithm. A robust semi-supervised learning algorithm based on maximum correntropy criterion (MCC), called GLR-MCC, is proposed to improve the robustness of GLR along with its convergence analysis. The half quadratic optimization technique is used to simplify the correntropy optimization problem to a standard semi-supervised problem in each iteration. Experimental results on typical machine learning data sets show that the proposed GLR-MCC can effectively improve the robustness of mislabeling noise and occlusion as compared with related semi-supervised learning algorithms.