As　an　effective　descriptor,　Symmetric　Positive　Definite　(SPD)　matrix　is　widely　used　in　several　areas　such　as　image　clustering.　Recently,　researchers　proposed　some　effective　methods　based　on　low　rank　theory　for　SPD　data　clustering　with　non-linear　metric.　However,　single　nuclear　norm　is　always　adopted　to　formulate　the　low　rank　model　in　these　methods,　which　would　lead　to　suboptimal　solution.　In　this　paper,　we　proposed　a　novel　double　low　rank　representation　method　for　SPD　clustering　problem,　in　which　matrix　factorization　and　non-convex　rank　constraint　are　combined　to　reveal　the　intrinsic　property　of　the　data　instead　of　employing　the　nuclear　norm.　Meanwhile,　kernel　method　and　Log-Euclidean　metric　are　combined　to　better　explore　the　intrinsic　geometry　within　SPD　data.　The　proposed　method　has　been　evaluated　on　several　public　datasets　and　the　experimental　results　demonstrate　that　the　proposed　method　outperforms　the　state-of-the-art　ones.