In　this　paper,　we　present　a　stabilized　finite　volume　element　method　with　the　conforming　finite　element　triples　P-1-P-0-P-1　and　P-1-P-1-P-1　for　approximating　the　velocity,　pressure,　and　hydraulic　head　of　a　coupled　Stokes-Darcy　problem.　The　proposed　method　is　convenient　to　implement,　computationally　efficient,　mass　conserving,　optimally　accurate,　and　able　to　handle　complex　geometries;　therefore,　this　method　has　great　potential　to　be　useful　for　realistic　problems　involving　coupled　free　flow　and　porous　media　flow.　To　offset　the　lack　of　the　inf-sup　condition　of　the　P-1-P-0　and　P-1-P-1　elements　for　the　Stokes　equation,　a　parameter　free　stabilization　term　is　added　to　the　discrete　formulation.　Stability　and　optimal　error　estimates　are　proved　based　on　a　bridge　built　up　between　the　finite　volume　element　method　and　the　finite　element　method.　An　element　level　implementation　of　the　stabilization　term　is　discussed　so　that　an　existing　code　package　can　be　conveniently　modified　to　handle　the　stabilization　procedures.　A　series　of　numerical　experiments　are　provided　to　illustrate　the　above　features　of　the　proposed　method,　the　theoretical　results,　and　the　realistic　applications.　(C)　2017　IMACS.　Published　by　Elsevier　B.V.　All　rights　reserved.