Hyperspectral　images　(HSIs)　are　often　degraded　by　different　kinds　of　noises.　Low　rank　(LR)-based　methods　have　achieved　great　performance　in　HSI　denoising　problem.　However,　the　LR-based　methods　only　consider　the　rank　of　the　whole　spectral　space,　conducting　no　constraints　on　the　intrinsic　structure　within　the　LR　space.　In　fact,　the　spectral　vectors　can　be　classified　into　different　categories　based　on　the　land-covers.　As　a　result,　the　spectral　space　can　be　modelled　as　a　union　of　multiple　LR　subspaces.　Regarding　this　structure,　we　introduce　the　framework　of　subspace　low　rank　(SLR)　representation　into　HSI　denoising　problem　and　propose　a　novel　SLR-based　denoising　method　for　HSIs.　Experiments　conducted　on　both　simulated　and　real　data　show　that　our　method　achieves　great　improvement　over　the　state-of-art　methods　qualitatively　and　quantitatively.　©　Springer　Nature　Singapore　Pte　Ltd.　2017.