Hyperspectral Images (HSIs) are usually degraded by many kinds of noise called mixed noise, which greatly limits the subsequent applications of HSIs. Many researches have proved the patch-based low-rank methods and the total variation (TV) based approaches have a good effect on reducing noise in HSIs. Here, we propose a non-local patch based rank-constraint HSIs noise suppression methods with a global 3-D anisotropic total variation (NLRATV). Differing from previous patch-based methods which usually ignore spatial structural information, we add more structural constraints with the non-local similarity across patches for suppressing the structural noise that exists at the same location of many bands. Besides, we utilize the global 3-D anisotropic total variation to ensure its smoothness in spatial and spectral dimensionalities while reconstructing the image. The augmented Lagrange multiplier method is adopted to optimize the proposed algorithm. The real data experiments have proved the superiority of NLRATV in decreasing mixed and dense noise. © Published under licence by IOP Publishing Ltd.