Nonnegative matrix factorization (NMF) and its various robust extensions have been widely applied to hyperspectral unmixing. Most existing robust NMF methods consider that noises only exist in one kind of formulation. However, hyperspectral images (HSI) are unavoidably corrupted by noisy bands and noisy pixels simultaneously in the real application s. This paper presents a robust NMF using ℓ_1,2 norm and further proposes a two-dimensional robust NMF model by incorporating ℓ_2,1 norm and ℓ_1,2 norm, which is robust to noises in both spatial dimension and spectral dimension simultaneously. In addition, the Huber's M-estimator is integrated into the model to achieve better assignations of weights for each pixel and band with various noise intensities, which avoids the singularity problem and effectively improves the unmixing performance. The elegant updating rules of the proposed model are also efficiently learnt and provided. Experiments are conducted on both synthetic and real hyperspectral data sets. The experimental results demonstrate the effectiveness of the proposed methods in unmixing performance.