Damped　outrigger　system　is　effective　for　improving　energy　dissipation　for　tall　buildings.　However,　conventional　damped　outrigger　(CDO)　system　with　viscous　damping　has　two　limitations:　(i)　its　maximum　damping　ratio　cannot　be　improved　when　outrigger/column　stiffness　is　inadequate;　(ii)　different　modes　achieve　their　maximum　damping　ratios　at　different　outrigger　damping　values,　and　thus　the　dampers　cannot　be　optimized　to　simultaneously　reduce　vibrations　of　multiple　modes　of　concern　to　their　minimum.　In　this　paper,　a　purely　frequency-independent　negative　stiffness　damped　outrigger　(FI-NSDO)　system　is　proposed　by　combining　frequency-independent　damper　(FID)　and　negative　stiffness　device　(NSD).　The　damped　outrigger　with　FID　can　achieve　the　maximum　damping　ratio　for　all　modes　as　compared　to　frequency-dependent　damper　like　viscous　damper.　As　the　NSD　has　the　features　of　assisting　and　enhancing　motion　and　frequency-independence,　the　utilization　of　NSD　will　considerably　improve　the　maximum　damping　ratios　when　outrigger/column　stiffness　is　inadequate　and　maintain　the　frequency-independent　feature　of　the　whole　system.　Therefore,　the　FI-NSDO　has　the　capability　of　simultaneously　increasing　the　damping　ratios　of　all　target　modes　to　their　maximum　values.　Analysis　in　frequency　domain　and　time　domain,　demonstrate　that　the　proposed　FI-NSDO　performs　better　in　controlling　the　multi-mode　vibration　of　seismic　responses.