Deep　Neural　Networks　(DNNs)　are　pervasively　used　in　a　large　number　of　applications,　such　as　Microsoft　Cortana,　Apple　Siri,　and　Google　Now.　The　traditional　method　is　to　offload　them　in　the　cloud,　which　causes　serious　data　transmission　delay　and　high　network　resource　cost,　as　well　as　user　privacy　leakage.　The　emergence　of　Mobile　Edge　Computing(MEC)　provides　a　new　solution　for　the　execution　of　DNN-based　applications.　With　the　increase　of　the　computing　power　of　mobile　devices　and　the　appearance　of　edge　nodes,　offloading　partial　layers　of　the　DNN-based　application　to　the　edge　will　speed　up　system　response,　reduce　the　burden　of　cloud　center　and　protect　privacy　of　users.　Most　of　existing　researches　focus　on　the　optimization　of　response　delay　for　DNN-based　applications　in　edge　computing　system,　but　there　is　no　mature　solution　to　the　cost　optimization　of　edge　computing　system.　To　effectively　reduce　the　cost　of　edge　computing　for　offloading　DNN-based　applications,　we　propose　a　offloading　strategy　based　on　Discrete　Particle　Swarm　Optimization　with　Genetic　Operators(DPSO-GO).　By　introducing　crossover　operator　and　mutation　operator　of　genetic　algorithm,　it　overcomes　the　defect　that　the　traditional　PSO　algorithm　is　easy　to　fall　into　local　optimum.　The　results　show　that　our　algorithm　can　reduce　the　cost　of　edge　computing　system　effectively　while　satisfying　the　delay　requirements　of　all　the　DNN-based　applications.　©　2019　IEEE.