Non-negative matrix factorization (NMF) is a classical hyperspectral unmixing model which minimizes the Euclidean distance between the hyperspectral data matrix and its low rank approximation (i.e., the product of endmember matrix and abundance matrix), and it fails when applied to noisy data because the loss function is sensitive to outliers. In this paper, we propose a Cauchy NMF (CauchyNMF) model for hyperspectral unmixing which uses a Cauchy loss function (CLF) to replace the traditional least-squares loss. Compared with the least-squares loss, CLF can penalize the noise term for suppressing the large noise mixed in the real data and thus is much more robust. Experimental results on simulated and real hyperspectral data sets demonstrate that our proposed CauchyNMF method is more accurate and robust than existing NMF methods, especially in the case of heavy noise.