Low　Rank　Representation　(LRR)　based　unsupervised　clustering　methods　have　achieved　great　success　since　these　methods　could　explore　low-dimensional　subspace　structure　embedded　in　original　data　effectively.　The　conventional　LRR　methods　generally　treat　the　data　as　the　points　in　Euclidean　space.　However,　it　is　no　longer　suitable　for　high-dimension　data　(such　as　video　or　imageset).　That　is　because　high-dimension　data　are　always　considered　as　non-linear　manifold　data　such　as　Grassmann　manifold.　Besides,　the　typical　LRR　methods　always　adopt　the　traditional　single　nuclear　norm　based　low　rank　constraint　which　can　not　fully　reveal　the　low　rank　property　of　the　data　representation　and　often　leads　to　suboptimal　solution.　In　this　paper,　a　new　LRR　based　clustering　model　is　constructed　on　Grassmann　manifold　for　high-dimension　data.　In　the　proposed　method,　each　high-dimension　data　is　formed　as　a　sample　on　Grassmann　manifold　with　non-linear　metric.　Meanwhile,　a　non-convex　low　rank　representation　is　adopt　to　reveal　the　intrinsic　property　of　these　high-dimension　data　and　reweighted　rank　minimization　constraint　is　introduced.　The　experimental　results　on　several　public　datasets　show　that　the　proposed　method　outperforms　the　state-of-the-art　clustering　methods.　©　2021,　Springer　Nature　Switzerland　AG.