In　this　paper,　an　adaptive　finite　element　method　is　proposed　for　solving　Kohn-Sham　equation　with　the　multilevel　correction　technique.　In　the　method,　the　Kohn-Sham　equation　is　solved　on　a　fixed　and　appropriately　coarse　mesh　with　the　finite　element　method　in　which　the　finite　element　space　is　kept　improving　by　solving　the　derived　boundary　value　problems　on　a　series　of　adaptively　and　successively　refined　meshes.　A　main　feature　of　the　method　is　that　solving　large　scale　Kohn-Sham　system　is　avoided　effectively,　and　solving　the　derived　boundary　value　problems　can　be　handled　efficiently　by　classical　methods　such　as　the　multigrid　method.　Hence,　the　significant　acceleration　can　be　obtained　on　solving　Kohn-Sham　equation　with　the　proposed　multilevel　correction　technique.　The　performance　of　the　method　is　examined　by　a　variety　of　numerical　experiments.　(C)　2017　Elsevier　Inc.　All　rights　reserved.