A model for Hyperspectral Image (HSI) restoration was proposed, which combines the L1 norm minimization of local patches and L1-2 Spatial-Spectral Total Variation (L1-2 SSTV) of global image. Firstly, the HSI was divided into local overlapping 3D patches, to reduce information loss caused by minimization of nuclear norm while improving local low-rank property. Secondly, the L1-2 SSTV regularization term with stronger sparse expression ability was proposed, to explore both spectral and spatial sparse prior simultaneously. Finally, the advantages of both worlds are combined, and a new HSI restoration model is proposed. The local norm is used to penalize spectrum low-rank term, and the L1-2 SSTV is used globally to constrain the spatial and spectral sparsity term of HSI, The model can not only effectively remove Gaussian noise, impulse noise, deadline and its mixture noise, but also reduce the dependence on the noise independent and identical distribution hypothesis, and can partially suppress the structure-related noise. Through a large number of experiments of simulated and real HSIs, and compared with the classical low-rank and total-variation-based restoration methods, experimental results were conducted to illustrate the advantage of the proposed method in HSI restoring, from visual/quantitative evaluations.