This　paper　deals　with　the　multi-hazard　vibration　reduction　of　high-rise　buildings　in　resisting　earthquakes　and　winds,　emphasizing　on　the　optimization　of　supplemental　negative　stiffness　damped　outrigger　(NSDO)　system.　Since　the　risks　of　wind　and　earthquake　are　both　inevitable,　the　competing　relationship　between　two　performance　indexes-harmful　inter-story　drift　and　structural　acceleration-of　tall　buildings　with　supplemental　NSDO　are　carefully　studied　concerning　along　wind,　cross　wind,　and　earthquake　loading.　As　an　energy　dissipation　outrigger　system,　NSDO　amplifies　the　deformation　of　viscous　damper　at　the　outrigger　ends,　thus　achieving　higher　efficiency　as　compared　to　conventional　damped　outrigger　(CDO)　systems.　The　resultant　superiority　of　NSDO　in　resisting　multi-hazard　is　then　verified.　For　example,　NSDO　provides　a　further　reduction　of　25.6%　in　seismic　harmful　drift　and　an　extra　22.3%　decrease　in　cross　wind　acceleration　response.　In　the　meantime,　NSDO　only　uses　about　1/3　of　the　outrigger　damping　coefficient　as　compared　to　CDO　systems.　Moreover,　NSDO　optimized　for　multi-hazard　can　achieve　a　good　tradeoff　design　without　compromising　too　much　for　one　specific　hazard.