Subspace　data　representation　has　recently　become　a　common　practice　in　many　computer　vision　tasks.　Low-rank　representation　(LRR)　is　one　of　the　most　successful　models　for　clustering　vectorial　data　according　to　their　subspace　structures.　This　paper　explores　the　possibility　of　extending　LRR　for　subspace　data　on　Grassmann　manifold.　Rather　than　directly　embedding　the　Grassmann　manifold　into　the　symmetric　matrix　space,　an　extrinsic　view　is　taken　to　build　the　self-representation　in　the　local　area　of　the　tangent　space　at　each　Grassmannian　point,　resulting　in　a　localized　LRR　method　on　Grassmann　manifold.　A　novel　algorithm　for　solving　the　proposed　model　is　investigated　and　implemented.　The　performance　of　the　new　clustering　algorithm　is　assessed　through　experiments　on　several　real-world　data　sets　including　MNIST　handwritten　digits,　ballet　video　clips,　SKIG　action　dips,　and　DynTex++　data　set　and　highway　traffic　video　clips.　The　experimental　results　show　that　the　new　method　outperforms　a　number　of　state-of-the-art　clustering　methods.