Modeling image sets as points on Grassmann manifold has attracted increasing interests in computer vision community and has been applied to many applications. However, such approaches have suffered from the limitation that high computational cost on Grassmann manifold must be involved, especially high-dimensional ones. In this paper, we propose an unsupervised robust dimensionality reduction algorithm for Grassmann manifold based on Neighborhood Preserving Embedding (GNPE). We first introduce two strategies to construct the coefficients-based similarity graph to eliminate the effects of errors. Then, a projection is learned from the high-dimensional Grassmann manifold to the relative low-dimensional one with more discriminative capability, where the local neighborhood structure is well preserved. To address the issue that the estimated similarity graph is unreliable with noise and outliers, we further propose a unified learning framework which performs similarity learning and projection learning simultaneously. By leveraging the interactions between these two essential tasks, we can capture accurate structures and learn discriminative projections. The proposed method can be optimized by an efficient iterative algorithm. Experiments on various image set classification and clustering tasks clearly show that our model achieves consistent improvements in terms of both effectiveness and efficiency.