In recent years, Nonnegative Matrix Factorization (NMF) methods for hyperspectral image unmixing have attracted widespread attention. However, due to the non-convexity of NMF problem, it cannot guarantee the uniqueness of the solution, and it is easy to fall into local minima. In order to reduce the solution space of NMF problem and improve the unmixing accuracy, a new method of reweighted sparse NMF (ARSNMF) was proposed. Firstly, considering the sparsity of abundance matrix, the sparse constraint was added to the NMF model. Then, considering that the calculation of the problem was complex and not easy to be optimized, it was converted into a form of reweighted sparse constraint, which not only achieved the sparse effect, but also solved the problem that was difficult to solve. In order to improve the convergence speed of the algorithm, the Alternating Direction Method of Multipliers (ADMM) was used to optimize the model, and the objective function was divided into several sub-problems for independent solution. Experiments based on simulation data and real data verify the effectiveness of the proposed algorithm.