Hyperspectral unmixing is one of the most important techniques in the remote sensing image analysis. In recent years, the nonnegative matrix factorization (NMF) method is widely used in hyperspectral unmixing. In order to solve the nonconvex problem of the NMF method, a number of constraints have been introduced into NMF models, including sparsity, manifold, smoothness, etc. However, these constraints ignore an important property of a hyperspectral image, i.e., the spectral responses in a homogeneous region are similar at each pixel but vary in different homogeneous regions. In this paper, we introduce a novel region-based structure preserving NMF (R-NMF) to explore consistent data distribution in the same region while discriminating different data structures across regions in the unmixed data. In this method, a graph cut algorithm is first applied to segment the hyperspectral image to small homogeneous regions. Then, two constraints are applied to the unmixing model, which preserve the structural consistency within the region while discriminating the differences between regions. Results on both synthetic and real data have validated the effectiveness of this method, and shown that it has outperformed several state-of-the-art unmixing approaches.