Deep　Neural　Networks　(DNNs)　have　become　an　essential　and　important　supporting　technology　for　smart　Internet-of-Things　(IoT)　systems.　Due　to　the　high　computational　costs　of　large-scale　DNNs,　it　might　be　infeasible　to　directly　deploy　them　in　energy-constrained　IoT　devices.　Through　offloading　computation-intensive　tasks　to　the　cloud　or　edges,　the　computation　offloading　technology　offers　a　feasible　solution　to　execute　DNNs.　However,　energy-efficient　offloading　for　DNN　based　smart　IoT　systems　with　deadline　constraints　in　the　cloud-edge　environments　is　still　an　open　challenge.　To　address　this　challenge,　we　first　design　a　new　system　energy　consumption　model,　which　takes　into　account　the　runtime,　switching,　and　computing　energy　consumption　of　all　participating　servers　(from　both　the　cloud　and　edge)　and　IoT　devices.　Next,　a　novel　energy-efficient　offloading　strategy　based　on　a　Self-adaptive　Particle　Swarm　Optimization　algorithm　using　the　Genetic　Algorithm　operators　(SPSO-GA)　is　proposed.　This　new　strategy　can　efficiently　make　offloading　decisions　for　DNN　layers　with　layer　partition　operations,　which　can　lessen　the　encoding　dimension　and　improve　the　execution　time　of　SPSO-GA.　Simulation　results　demonstrate　that　the　proposed　strategy　can　significantly　reduce　energy　consumption　compared　to　other　classic　methods.