Nonnegative matrix factorization (NMF) is a widely used hyperspectral unmixing model which decomposes a known hyperspectral data matrix into two unknown matrices, i.e., endmember matrix and abundance matrix. Due to the use of least-squares loss, the NMF model is usually sensitive to noise or outliers. To improve its robustness, we introduce a general robust loss function to replace the traditional least-squares loss and propose a general loss-based NMF (GLNMF) model for hyperspectral unmixing in this letter. The general loss function is a superset of many common robust loss functions and is suitable for handling different types of noise. Experimental results on simulated and real hyperspectral data sets demonstrate that our GLNMF model is more accurate and robust than existing NMF methods.