For　the　hyperspectral　image(HSI)　denoising　problem,　we　propose　a　group-based　low　rank　representation　(GLRR)　method.　A　corrupted　HSI　is　divided　into　overlapping　patches　and　the　similar　patches　are　combined　into　a　group.　The　group　is　de-noised　as　a　whole　using　low　rank　representation(LRR).　Our　method　can　employ　both　the　local　similarity　within　the　patch　and　the　nonlocal　similarity　across　the　patches　within　a　group　simultaneously,　while　nonlocal　similar　patches　within　the　group　can　bring　extra　structure　information　for　the　corrupted　patch,　which　makes　the　noise　more　significant　to　be　detected　as　outliers.　Since　the　uncorrupted　patches　have　an　intrinsic　low-rank　structure,　LRR　is　employed　for　the　denoising　of　the　patch　group.　Both　simulated　and　real　data　are　used　in　the　experiments.　The　effectiveness　of　our　method　is　proved　both　qualitatively　and　quantitatively.　©　2015　IEEE.