This　study　presents　a　new　crosswind　mitigation　strategy　by　using　negative　stiffness　damped　outrigger　(NSDO)　system　for　tall　buildings.　Using　the　＇assisting　motion＇　feature　of　negative　stiffness,　NSDO　amplifies　the　motion　of　viscous　damper　resulting　in　and　significant　improvement　of　energy　dissipation　for　tall　buildings.　Systematical　evaluation　and　comparison　on　crosswind　performance　are　carried　out　for　tall　buildings　using　(a)　conventional　outrigger　(CO),　(b)　conventional　damped　outrigger　(CDO),　and　(c)　NSDO.　It　is　shown　that　the　proposed　NSDO　is　able　to　achieve　a　damping　amplification　factor　larger　than　a　unit,　which　would　never　be　achieved　by　CDO　in　practical　due　to　the　actual　deformation　of　perimeter　columns.　In　this　way,　NSDO　has　the　most　satisfactory　crosswind　reduction　effect,　especially　when　perimeter　column　stiffness　is　insufficient.　For　example,　replacing　CDO　with　NSDO　not　only　attenuates　crosswind-induced　harmful　drift　and　structural　acceleration　by　22%　and　36%,　respectively,　but　also　further　saves　about　75%　of　the　size　of　viscous　dampers.　In　other　words,　NSDO　adopts　less　outrigger　damping　coefficient　but　reduces　more　crosswind-induced　vibration.　©　2022　John　Wiley　&　Sons　Ltd.