It　is　a　challenging　problem　to　cluster　multi-and　high-dimensional　data　with　complex　intrinsic　properties　and　nonlinear　manifold　structure.　The　recently　proposed　subspace　clustering　method,　Low　Rank　Representation　(LRR),　shows　attractive　performance　on　data　clustering,　but　it　generally　does　with　data　in　Euclidean　spaces.　In　this　paper,　we　intend　to　cluster　complex　high　dimensional　data　with　multiple　varying　factors.　We　propose　a　novel　representation,　namely　Product　Grassmann　Manifold　(PGM),　to　represent　these　data.　Additionally,　we　discuss　the　geometry　metric　of　the　manifold　and　expand　the　conventional　LRR　model　in　Euclidean　space　onto　PGM　and　thus　construct　a　new　LRR　model.　Several　clustering　experimental　results　show　that　the　proposed　method　obtains　superior　accuracy　compared　with　the　clustering　methods　on　manifolds　or　conventional　Euclidean　spaces.