Two-dimensional locality preserving projections (2DLPP) that use 2D image representation in preserving projection learning can preserve the intrinsic manifold structure and local information of data. However, 2DLPP is based on the Euclidean distance, which is sensitive to noise and outliers in data. In this paper, we propose a novel locality preserving projection method called nuclear norm-based two-dimensional locality preserving projections (NN-2DLPP). First, NN-2DLPP recovers the noisy data matrix through low-rank learning. Second, noise in data is removed and the learned clean data points are projected on a new subspace. Without the disturbance of noise, data points belonging to the same class are kept as close to each other as possible in the new projective subspace. Experimental results on six public image databases with face recognition, object classification, and handwritten digit recognition tasks demonstrated the effectiveness of the proposed method.