Summary: Based on manifold regularization, we develop a novel algorithm called Semi-supervised Convex Nonnegative Matrix Factorization (SCNMF). SCNMF can capture the data intrinsic geometric structure with within-class graph and between-class graph. The proposed algorithm not only has the characteristics of data matrix convex factorization, but also preserves geometric structure and discriminant analysis. Finally, experimental results demonstrate that it achieves encouraging results on face data sets.