This　study　proposes　a　novel　multi-view　soft　block　diagonal　representation　framework　for　clustering　complete　and　incomplete　multi-view　data.　First,　given　that　the　multi-view　self-representation　model　offers　better　performance　in　exploring　the　intrinsic　structure　of　multi-view　data,　it　can　be　nicely　adopted　to　individually　construct　a　graph　for　each　view.　Second,　since　an　ideal　block　diagonal　graph　is　beneficial　for　clustering,　a　＇soft＇　block　diagonal　affinity　matrix　is　constructed　by　fusing　multiple　previous　graphs.　The　soft　diagonal　block　regulariser　encourages　a　matrix　to　approximately　have　(not　exactly)　K　diagonal　blocks,　where　K　is　the　number　of　clusters.　This　strategy　adds　robustness　to　noise　and　outliers.　Third,　to　handle　incomplete　multi-view　data,　multiple　indicator　matrices　are　utilised,　which　can　mark　the　position　of　missing　elements　of　each　view.　Finally,　the　alternative　direction　of　multipliers　algorithm　is　employed　to　optimise　the　proposed　model,　and　the　corresponding　algorithm　complexity　and　convergence　are　also　analysed.　Extensive　experimental　results　on　several　real-world　datasets　achieve　the　best　performance　among　the　state-of-the-art　complete　and　incomplete　clustering　methods,　which　proves　the　effectiveness　of　the　proposed　methods.