We　have　studied　the　adsorption　of　sulfur　at　regular　and　defect　sites　of　the　MgO　(001)　surface　using　cluster　models　embedded　in　a　large　array　of　point　charges　by　the　density　functional　method.　The　calculated　results　indicate　that　it　is　a　chemical　adsorption　regarding　sulfur　at　both　the　regular　site　and　the　defect　site　of　the　MgO　(001)　surface.　Especially　for　sulfur　adsorbed　at　different　oxygen　vacancy　sites　(F,　F+　and　F2+　centers)　and　different　magnesium　vacancy　sites　(V,　V-　and　V2-　centers),　it　has　very　large　adsorption　energies,　which　reflects　the　fact　that　the　MgO　(001)　surface　with　the　vacancies　is　an　excellent　adsorbent　for　sulfur　adsorption.　Besides,　we　find　that　the　adsorbed　sulfur　is　almost　inserted　into　the　lattice　for　sulfur　adsorbed　at　the　magnesium　vacancy　site　of　the　MgO　(001)　surface.　The　adsorption　energy　of　sulfur　on　the　MgO　(001)　surface　with　magnesium　vacancies　is　much　larger　when　compared　to　that　on　the　MgO　(001)　surface　with　oxygen　vacancies.　At　the　same　time,　it　is　also　found　that　the　S　behaves　as　an　electron　acceptor　except　that　it　is　adsorbed　at　the　magnesium　vacancy　site　behaving　as　an　electron　donor.