The　sparse　subspace　clustering　problem　is　to　group　a　set　of　data　into　their　underlying　subspaces　and　correct　the　underlying　noise　simultaneously.　It　was　shown　in　the　recent　literature　that,　the　clustering　task　can　be　characterized　as　a　block　diagonal　matrix　regularized　nonconvex　minimization　problem.　However,　this　problem　is　not　easy　to　solve　because　it　contains　a　nonconvex　bilinear　function.　The　earliest　method　named　block　diagonal　regularization　(BDR)　only　solved　a　penalized　model,　but　not　the　original　problem　itself.　The　recently　algorithm　named　accelerated　block　coordinated　gradient　descent　(ABCGD)　can　solve　the　original　problem　efficiently,　but　its　convergence　is　not　given.　In　this　paper,　we　attempt　to　use　an　accelerated　gradient　method　(AGM),　and　establish　its　convergence　in　the　sense　of　converging　to　a　critical　point　with　a　certain　stepsize　policy.　We　show　that　closed-form　solutions　are　enjoyed　for　each　subproblem　by　taking　full　use　of　the　constraints＇　structure　so　that　the　algorithm　is　easily　implementable.　Finally,　we　do　numerical　experiments　by　the　using　of　two　real　datasets.　The　numerical　results　illustrate　that　the　proposed　algorithm　AGM　performs　better　than　BDR　and　ABCGD　evidently.