Purpose　The　present　paper　addresses　the　vibration　reduction　for　an　elastic　beam　with　an　asymmetric　boundary　condition　that　is　clamped　at　one　end　and　elastically　supported　at　the　other　end.　An　inertial　nonlinear　energy　sink　(NES)　is　installed　on　the　elastic　support　end　to　suppress　the　beam＇s　vibration.　Methods　The　nonlinear　terms　introduced　by　the　NES　are　transferred　as　the　external　excitations　acting　on　the　beam.　The　motion　equations　of　the　beam　with　an　NES　are　derived　according　to　Hamilton＇s　principle　and　the　Galerkin　truncation　method.　The　beam＇s　natural　frequencies　and　corresponding　mode　shapes　are　analytically　obtained　and　verified　with　the　results　of　the　finite　element　method.　The　responses　of　the　beam　are　numerically　and　analytically　solved　by　the　fourth　order　Runge-Kutta　method　and　the　harmonic　balance　method　(HBM),　respectively.　Results　The　good　agreement　among　the　results　validates　the　present　derivation　of　the　theoretical　model　and　numerical　solutions.　The　steady-state　responses　of　the　beam　with　and　without　the　NES　are　compared　and　analyzed　in　the　time　domain.　Conclusions　The　results　demonstrate　that　adding　the　inertial　enhanced　NES　can　effectively　reduce　the　resonance　amplitude　of　the　beam.　Furthermore,　a　parametric　optimization　is　conducted　for　NES　to　improve　its　performance.　The　results　of　this　paper　contribute　to　the　application　of　NESs　on　the　boundaries　of　elastic　structures.