In　this　paper,　a　stabilized　mixed　finite　element　method　for　a　coupled　steady　Stokes-Darcy　problem　is　proposed　and　investigated.　This　method　is　based　on　two　local　Gauss　integrals　for　the　Stokes　equations.　Its　originality　is　to　use　a　difference　between　a　consistent　mass　matrix　and　an　under-integrated　mass　matrix　for　the　pressure　variable　of　the　coupled　Stokes-Darcy　problem　by　using　the　lowest　equal-order　finite　element　triples.　This　new　method　has　several　attractive　computational　features:　parameter　free,　flexible,　and　altering　the　difficulties　inherited　in　the　original　equations.　Stability　and　error　estimates　of　optimal　order　are　obtained　by　using　the　lowest　equal-order　finite　element　triples　(P-1　-　P-1　-　P-1)　and　(Q(1)　-　Q(1)　-　Q(1))　for　approximations　of　the　velocity,　pressure,　and　hydraulic　head.　Finally,　a　series　of　numerical　experiments　are　given　to　show　that　this　method　has　good　stability　and　accuracy　for　the　coupled　problem　with　the　Beavers-Joseph-Saffman-Jones　and　Beavers-Joseph　interface　conditions.　(C)　2015　Elsevier　B.V.　All　rights　reserved.