Wireless　Body　Area　Network　(WBAN)　as　one　of　the　primary　Internet　of　Things　(IoT)　provides　real　time　and　continuous　healthcare　monitoring　and　has　been　widely　deployed　to　improve　the　quality　of　peoples＇　life.　In　edge-enabled　WBANs,　intensive　computing　tasks　could　be　offloaded　to　Mobile　Edge　Computing　(MEC)　servers,　guaranteeing　that　the　massive　amount　of　health　data　with　different　user　priorities　could　be　processed　in　lower　delay　and　energy　consumption.　Efficient　computation　offloading　schemes　are　more　critical　to　satisfy　the　massive　data　access　and　personalized　service　requirements　for　multiple　Quality　of　Service　(QoS)　parameters　constraint　WBANs.　In　this　paper,　we　propose　a　Two-Stage　Potential　Game　based　Computation　Offloading　Strategy　(TPOS)　to　optimize　resource　allocation　while　taking　into　consideration　the　task　priorities　and　user　priorities　of　WBANs.　Firstly,　we　construct　a　system　utility　maximization　problem　about　the　QoS　of　tasks.　The　reward,　cost　and　penalty　functions　are　given　to　model　the　computation　offloading.　Then,　we　propose　a　two-stage　optimization　method　to　solve　the　problem　of　mutual　restriction　strategies　existing　in　the　strategy　space　of　the　potential　game　model,　reducing　the　computation　complexity　and　improving　the　feasibility　of　the　algorithm.　Finally,　performance　evaluations　on　average　processing　delay,　energy　consumption　and　network　utility　are　conducted　to　show　the　significance　of　the　proposed　TPOS　algorithm.