With　the　rapid　development　of　mobile　Internet　and　increasing　numbers　of　mobile　devices,　mobile　edge　computing　(MEC)　which　offers　computational　capability　within　radio　access　network　has　become　the　key　technology　to　enhance　users＇　experience.　In　this　paper,　we　investigate　the　computing　offloading　problem　considering　delay　and　energy　consumption　of　mobile　devices　jointly　in　wireless　access　network.　Then,　the　optimization　problem　minimizing　the　delay　and　energy　consumption　of　mobile　devices　is　formulated　and　transformed　into　convex　optimization.　To　solve　the　optimization,　a　delay　and　energy　consumption　efficient　offloading　algorithm　(DEOA)　based　on　alternating　direction　method　of　multipliers　(ADMM)　is　proposed.　The　simulation　results　show　that　the　proposed　algorithm　significantly　reduces　delay　and　energy　consumption　compared　to　stochastic　allocation.　Meanwhile,　compared　with　joint　delay　and　energy　efficient　offloading　scheme　(JCDE)　proposed　in　another　paper,　the　consumption　is　reduced　while　the　average　speed　of　solution　is　increased　by　about　65%　under　various　system　parameters.　©　2019　IEEE.