Traditional nonnegative matrix factorization (NMF) applied to hyper-spectral unmixing is susceptible to the interference of pretzel noise, resulting in unmixing failure. Previous sparse unmixing requires determining the optimal feature subset in a spatial domain involving more dispersed information and susceptibility to noise. The weighted sparse Cauchy-nonnegative matrix factorization (SSCNMF) algorithm based on the spatial-spectral constraints is proposed to solve these problems. First, the Cauchy loss-function-based NMF model, which exhibits excellent robustness in suppressing extreme outliers, is applied. Second, an adaptive sparse weighting factor is introduced to improve the sparsity of the abundance matrix. A spatial-spectral constraint term is added, in which the spectral factor is used to measure the sparsity of abundance among different spectra. The spatial factor exploits the smoothness of the spatial domain of abundance to improve the extraction efficiency of data features. Simulation experiments were conducted on simulated and actual datasets. The effectiveness and excellent anti-noise performance of the SSCNMF algorithm are verified by comparing it with some classical hyper-spectral unmixing algorithms.