Hypersepctral unmixing (HU) has been one of the most challenging tasks in hyperspectral image research. Recently, nonnegative matrix factorization (NMF) has shown its superiority in hyperspectral unmixing due to its flexible modeling and little prior requirement. But most NMF algorithms tend to use least square function as the objective, which is sensitive to outliers and different kinds of noise. In this article, we propose a modified Huber (mHuber) NMF model to achieve robustness to outliers and different kinds of noise. Under this robust model, we accelerate the half-quadratic optimization algorithm by replacing multiplicative updating rule with a projected nonlinear conjugated gradient rule, which achieves much faster convergence rate. Moreover, a new tuning parameter, rather than a fixed one, is given to adapt to mHuber loss function. Finally, we perform algorithm analysis and experiments in the synthetic and real-world datasets, which confirms the effectiveness and superiority of the proposed method when compared with several state-of-the-art NMF methods in HU.