A　deep　neural　network　(DNN)　has　become　increasingly　popular　in　industrial　Internet　of　Things　scenarios.　Due　to　high　demands　on　computational　capability,　it　is　hard　for　DNN-based　applications　to　directly　run　on　intelligent　end　devices　with　limited　resources.　Computation　offloading　technology　offers　a　feasible　solution　by　offloading　some　computation-intensive　tasks　to　the　cloud　or　edges.　Supporting　such　capability　is　not　easy　due　to　two　aspects:　Adaptability:　offloading　should　dynamically　occur　among　computation　nodes.　Effectiveness:　it　needs　to　be　determined　which　parts　are　worth　offloading.　This　article　proposes　a　novel　approach,　called　DNNOff.　For　a　given　DNN-based　application,　DNNOff　first　rewrites　the　source　code　to　implement　a　special　program　structure　supporting　on-demand　offloading　and,　at　runtime,　automatically　determines　the　offloading　scheme.　We　evaluated　DNNOff　on　a　real-world　intelligent　application,　with　three　DNN　models.　Our　results　show　that,　compared　with　other　approaches,　DNNOff　saves　response　time　by　12.4-66.6%　on　average.