To　explore　the　application　of　traditional　tuned　mass　dampers　(TMDs)　to　the　earthquake　induced　vibration　control　problem,　a　pounding　tuned　mass　damper　(PTMD)　is　proposed　by　adding　a　viscoelastic　limitation　to　the　traditional　TMD.　In　the　proposed　PTMD,　the　vibration　energy　can　be　further　dissipated　through　the　impact　between　the　attached　mass　and　the　viscoelastic　layer.　More　energy　dissipation　modes　can　guarantee　better　control　effectiveness　under　a　suite　of　excitations.　To　further　reduce　mass　ratio　and　enhance　the　implementation　of　the　PTMD　control,　multiple　PTMDs　(MPTMD)　control　is　then　presented.　After　the　experimental　validation　of　the　proposed　improved　Hertz　based　pounding　model,　the　basic　equations　of　the　MPTMD　controlled　system　are　obtained.　Numerical　simulation　is　conducted　on　the　benchmark　model　of　the　Canton　Tower.　The　control　effectiveness　of　the　PTMD　and　the　MPTMD　is　analyzed　and　compared　under　different　earthquake　inputs.　The　sensitivity　and　the　optimization　of　the　design　parameters　are　also　investigated.　It　is　demonstrated　that　PTMDs　have　better　control　efficiency　over　the　traditional　TMDs,　especially　under　more　severe　excitation.　The　control　performance　can　be　further　improved　with　MPTMD　control.　The　robustness　can　be　enhanced　while　the　attached　mass　for　each　PTMD　can　be　greatly　reduced.　It　is　also　demonstrated　through　the　simulation　that　a　non-uniformly　distributed　MPTMD　has　better　control　performance　than　the　uniformly　distributed　one.　Parameter　study　is　carried　out　for　both　the　PTMD　and　the　MPTMD　systems.　Finally,　the　optimization　of　the　design　parameters,　including　mass　ratio,　initial　gap　value,　and　number　of　PTMD　in　the　MPTMD　system,　is　performed　for　control　improvement.