To　improve　the　convenience　of　the　traditional　tuned　mass　damper(TMD),　tuned　inerter　damper　(TID)　is　proposed　to　mitigate　the　vibration　of　the　structure　subjected　to　ground　white　noise.　The　corresponding　optimal　damping　parameter,　optimal　stiffness　parameter　and　displacement　variance　analytical　expression　are　deduced.　The　formulas　show　that　the　optimum　parameters　relate　to　the　square　of　the　mode　difference　between　adjacent　floors.　The　larger　difference,　the　better　control　effectiveness.　Then,　TID　is　applied　on　three　uniform　structure　and　one　non-uniform　structure.　The　results　indicate　that　TID　performs　well　on　the　median　and　low　buildings　and　it　is　also　suitable　for　high　mode　control.　TID-TMD　works　much　better　than　TID　in　seismic　reduction　and　when　the　structure　is　subjected　to　earthquakes　exercitation,　but　they　are　neck　and　neck　as　a　whole.　So,　TMD　s　only　installed　at　the　top　floor　with　TID　set　up　other　floors,　which　solves　the　problems　such　as　spatial　occupation,　inconvenient　installment　and　heavy　mass.　©　2018,　Editorial　Department　of　JVMD.　All　right　reserved.