Mobile　user　devices,　such　as　smartphones　or　laptops,　run　increasingly　complex　applications　that　require　more　computing　power　and　more　computing　resources.　However,　the　battery　capacity　and　energy　consumption　of　mobile　devices　limit　these　developments.　Mobile-Edge　Computing　(MEC)　is　a　technology　that　utilizes　wireless　network　to　provide　IT　and　cloud　computing　services　for　nearby　users.　IT　can　build　a　network　environment　with　low　latency　and　high　bandwidth　and　accelerate　the　response　speed　of　network　services.　Transferring　computing　tasks　of　mobile　devices　to　MEC　server　through　task　migration　technology　can　effectively　relieve　computing　pressure　of　devices.　Efficient　task　migration　method　can　minimize　the　energy　consumption　of　mobile　devices　on　the　basis　of　ensuring　the　data　delay　requirement.　According　to　the　characteristics　of　coarse-grained　task　migration　in　current　mobile　edge　computing,　this　paper　proposes　a　finegrained　task　migration　scheme　based　on　Ant　Colony　Algorithm(ACO),　aiming　to　minimize　the　energy　consumption　of　mobile　devices　on　the　basis　of　strict　delay　constraints　in　mobile　applications.　Finally,　experimental　results　show　that　the　method　used　in　this　paper　can　effectively　reduce　the　energy　consumption　of　mobile　devices　by　26%,　compared　to　the　static　strategy.　©　2020　ACM.