Hyperspectral　images　(HSIs)　have　been　used　in　a　wide　range　of　fields,　such　as　agriculture,　food　safety,　mineralogy,　and　environment　monitoring,　but　being　corrupted　by　various　kinds　of　noise　limits　its　efficacy.　Low-rank　representation　(LRR)　has　proved　its　effectiveness　in　the　denoising　of　HSIs.　However,　it　just　employs　local　information　for　denoising,　which　results　in　ineffectiveness　when　local　noise　is　heavy.　In　this　paper,　we　propose　an　approach　of　group　low-rank　representation　(GLRR)　for　the　HSI　denoising.　In　our　GLRR,　a　corrupted　HSI　is　divided　into　overlapping　patches,　the　similar　patches　are　combined　into　a　group,　and　the　group　is　reconstructed　as　a　whole　using　LRR.　The　proposed　method　enables　the　exploitation　of　both　the　local　similarity　within　a　patch　and　the　nonlocal　similarity　across　the　patches　in　a　group　simultaneously.　The　additional　non-locally　similar　patches　can　bring　in　extra　structural　information　to　the　corrupted　patches,　facilitating　the　detection　of　noise　as　outliers.　LRR　is　applied　to　the　group　of　patches,　as　the　uncorrupted　patches　enjoy　intrinsic　low-rank　structure.　The　effectiveness　of　the　proposed　GLRR　method　is　demonstrated　qualitatively　and　quantitatively　by　using　both　simulated　and　real-world　data　in　experiments.