Group　signature　is　a　cryptography　primitive　that　has　been　widely　researched.　It　strikes　a　balance　between　digital　signature　and　the　user＇s　demand　for　anonymity.　A　valid　member　in　the　group　can　generate　a　signature　on　behalf　of　the　whole　group.　The　public　can　only　know　that　it　was　provided　by　a　valid　group　member　and　learn　nothing　about　the　actual　identity　of　the　signer　when　verifying　a　group　signature.　Backes　et　al　pointed　out　that　the　existing　dynamic　group　signature　schemes　implicitly　assume　that　the　membership　of　everyone　in　the　group　is　open　to　the　public.　Thus,　they　put　forward　a　property　called　membership　privacy　for　dynamic　group　signature.　In　this　paper,　we　design　a　dynamic　group　signature　scheme　with　membership　privacy　on　top　of　Signature　Proofs　of　Knowledge　(SPK)　and　BBS+　signature.　Further　more,　dynamic　accumulator　mechanism　is　adopted　to　revoke　a　group　member＇s　authority　to　sign.　Then,　a　security　analysis　demonstrates　that　the　proposed　group　signature　scheme　satisfies　join-leave　privacy.　Finally,　quantitative　analysis　and　experimental　results　show　that　the　proposed　group　signature　scheme　achieves　the　fewer　signature　size　and　less　computation　overhead　compared　with　Backes＇s　scheme.