The Partial Least Squares (PLS) algorithm has been widely applied in face recognition in recent years. However, all the improved algorithms of PLS did not utilize non-negativity and sparsity synchronously to improve the recognition accuracy and robustness. In order to solve these problems, this paper proposes a novel algorithm named TwoDimension Non-negative Sparse Partial Least Squares (2DNSPLS), which incorporates the constraints of nonnegativity and sparse to 2DPLS while extracting the facial features. Consequently, not only do the features extracted by 2DNSPLS contain the label information, as well as the internal structure of image matrix, but they also contain local non-negative interpretability and sparsity.For evaluating the approach's performance, a series of experiments are conducted on the Yale and the PIE face databases, which demonstrate that the proposed approach outperforms the state-of-art algorithms and has good robustness to occlusion.