The　deep　subspace　clustering　method,　which　adopts　deep　neural　networks　to　learn　a　representation　matrix　for　subspace　clustering,　has　shown　good　performance.　However,　this　representation　matrix　ignores　the　structural　constraint　when　it　is　applied　to　subspace　clustering.　It　is　known　that　samples　from　different　classes　can　be　taken　as　embedding　in　independent　subspaces.　Thus,　the　representation　matrix　should　have　a　block　diagonal　structure.　This　paper　presents　the　Deep　Subspace　Clustering　with　Block　Diagonal　Constraint　(DSC-BDC),　a　model　which　constrains　the　representation　matrix　with　block　diagonal　structure　and　gives　a　block　diagonal　regularizer　for　learning　a　suitable　representation.　Furthermore,　to　enhance　the　representation　capacity,　DSC-BDC　reforms　the　block-diagonal　structure　constraint　by　performing　a　separation　strategy　on　the　representation　matrix.　Specifically,　the　separation　strategy　ensures　that　the　most　compact　samples　are　selected　to　the　represent　data.　An　alternative　optimization　algorithm　is　designed　for　our　model.　Extensive　experiments　on　four　public　and　real-world　databases　demonstrate　the　effectiveness　and　superiority　of　our　proposed　model.