Spectral unmixing can effectively improve the utilization efficiency of hyperspectral images. Nonnegative matrix factorization is frequently used to find linear representations of nonnegative data, which can effectively solve the problem of mixed pixels. A hyperspectral unmixing algorithm is proposed based on the sparsity of abundance and local invariance of an image. A new objective function is constructed by adopting the sparsity regularization term of abundance and the graph regularization term of the Laplacian matrix. Better unmixing results are obtained after several iterations of the endmembers and abundance. The proposed algorithm is validated using both simulation and real data, and the experimental results demonstrate that the proposed algorithm exhibits good performance.