In　recent　years,　the　delay-sensitive　and　computationally　intensive　applications　have　been　popular　in　the　wireless　mobile　terminal　domain.　Meanwhile,　spectrum　resource　and　computational　capability　of　mobile　terminals　are　limited.　These　factors　limit　the　quality　of　service　(QoS)　of　wireless　communication　networks.　Mobile　Edge　Computing　(MEC)　has　become　the　technology　to　solve　these　problems.　In　the　MEC　system,　mobile　terminals　can　offload　their　tasks　to　MEC　server　in　order　to　reduce　latency　and　save　terminals＇　battery.　During　computation　offloading,　spectrum　allocation　is　important,　this　paper　formulates　an　optimization　problem　as　linear　programming　(LP)　form　for　minimizing　energy　consumption.　Then　we　solve　the　problem　via　the　alternating　direction　method　of　multipliers　(ADMM)　algorithm　in　order　to　solve　the　optimization　problem　efficiently.　Finally,　simulation　results　indicate　that　our　proposed　method　efficiently　save　energy　consumption　to　meet　green　communication　requirements.　©　2019　IEEE.