Hyperspectral image (HSI) unmixing has attracted increasing research interests in recent decades. The major difficulty of it lies in that the endmembers and the associated abundances need to be separated from highly mixed observation data with few a priori information. Recently, sparsity-constrained nonnegative matrix factorization (NMF) algorithms have been proved effective for hyperspectral unmixing (HU) since they can sufficiently utilize the sparsity property of HSIs. In order to improve the performance of NMF-based unmixing approaches, spectral and spatial constrains have been added into the unmixing model, but spectral-spatial joint structure is required to be more accurately estimated. To exploit the property that similar pixels within a small spatial neighborhood have higher possibility to share similar abundances, hypergraph structure is employed to capture the similarity relationship among the spatial nearby pixels. In the construction of a hypergraph, each pixel is taken as a vertex of the hypergraph, and each vertex with its k nearest spatial neighboring pixels form a hyperedge. Using the hypergraph, the pixels with similar abundances can be accurately found, which enables the unmixing algorithm to obtain promising results. Experiments on synthetic data and real HSIs are conducted to investigate the performance of the proposed algorithm. The superiority of the proposed algorithm is demonstrated by comparing it with some state-of-The-Art methods.