Due　to　the　high　demands　of　deep　neural　network　(DNN)　based　applications　on　computational　capability,　it　is　hard　for　them　to　be　directly　run　on　mobile　devices　with　limited　resources.　Computation　offloading　technology　offers　a　feasible　solution　by　offloading　some　computation-intensive　tasks　of　neural　network　layers　to　edges　or　remote　clouds　that　are　equipped　with　sufficient　resources.　However,　the　offloading　process　might　lead　to　excessive　delays　and　thus　seriously　affect　the　user　experience.　To　address　this　important　problem,　we　first　regard　the　average　response　time　of　multi-task　parallel　scheduling　as　our　optimization　goal.　Next,　the　problem　of　computation　offloading　and　task　scheduling　for　DNN-based　applications　in　cloud-edge　computing　is　formulated　with　a　scheme　evaluation　algorithm.　Finally,　the　greedy　and　genetic　algorithms　based　methods　are　proposed　to　solve　the　problem.　The　extensive　experiments　are　conducted　to　demonstrate　the　effectiveness　of　the　proposed　methods　for　scheduling　tasks　of　DNN-based　applications　in　different　cloud-edge　environments.　The　results　show　that　the　proposed　methods　can　obtain　the　near-optimal　scheduling　performance,　and　generate　less　average　response　time　than　traditional　scheduling　schemes.　Moreover,　the　genetic　algorithm　leads　to　less　average　response　time　than　the　greedy　algorithm,　but　the　genetic　algorithm　needs　more　running　time.　©　2013　IEEE.