An　hybrid　scheme　comprised　of　Nonlinear　Energy　Sinks　(NES)　and　Tuned　Mass　Damper(TMD)　is　proposed　to　suppress　the　vibration　of　the　structure.　The　equation　of　slow　dynamics　system　and　the　analytical　energy　prediction　equation　are　formulated　using　the　complex-averaging　method　and　the　multi-scale　method.　The　derived　energy　equation　shows　cubic　function　relationship　in　the　energy　between　main　structure　and　NES,　and　linear　relationship　between　TMD　and　main　structure.　The　numerical　simulation　indicates　that　the　phenomenon　of　targeted　energy　transfer　can　be　produced　quickly　in　NES　of　the　hybrid　system,　and　high　energy　consumption　rate　is　achieved　in　the　whole　system　compared　with　the　pure　NES　control;　It　is　also　demonstrated　that　theoretical　analysis　is　correct　since　the　curves　of　numerical　calculations　vary　around　the　analytical　prediction　values;　Besides,　not　only　wide　frequency　band　but　also　low　sensitivity　can　be　obtained　by　the　hybrid　scheme　because　of　its　good　robustness.　©　2017,　Engineering　Mechanics　Press.　All　right　reserved.