Many　application　scenarios　involve　sequential　data,　but　most　existing　clustering　methods　do　not　well　utilize　the　order　information　embedded　in　sequential　data.　In　this　paper,　we　study　the　subspace　clustering　problem　for　sequential　data　and　propose　a　new　clustering　method,　namely　ordered　sparse　clustering　with　block-diagonal　prior　(BD-OSC).　Instead　of　using　the　sparse　normalizer　in　existing　sparse　subspace　clustering　methods,　a　quadratic　normalizer　for　the　data　sparse　representation　is　adopted　to　model　the　correlation　among　the　data　sparse　coefficients.　Additionally,　a　block-diagonal　prior　for　the　spectral　clustering　affinity　matrix　is　integrated　with　the　model　to　improve　clustering　accuracy.　To　solve　the　proposed　BD-OSC　model,　which　is　a　complex　optimization　problem　with　quadratic　normalizer　and　block-diagonal　prior　constraint,　an　efficient　algorithm　is　proposed.　We　test　the　proposed　clustering　method　on　several　types　of　databases,　such　as　synthetic　subspace　data　set,　human　face　database,　video　scene　clips,　motion　tracks,　and　dynamic　3-D　face　expression　sequences.　The　experiments　show　that　the　proposed　method　outperforms　state-of-the-art　subspace　clustering　methods.