This　paper　investigated　the　fragility　and　inelastic　performance　of　steel　braced-core-tube　frame　outrigger　(SBFO)　tall　buildings　with　passive　adaptive　negative　stiffness　damped　outrigger　(ANSDO)　systems.　The　proposed　A-NSDO　provided　passive　negative　stiffness　to　achieve　substantial　damping　effect　for　tall　buildings　at　elastic　stage.　Once　tall　buildings　was　subjected　to　excessive　earthquakes　and　yielded,　the　A-NSDO　was　capable　of　stiffening　the　connection　between　outrigger　ends　and　perimeter　columns　passively　and　adaptively　to　guarantee　the　integrity　of　tall　buildings.　Passive　configuration　and　working　mechanism　of　the　A-NSDO　were　introduced　and　then　its　adaptive　behavior　was　validated　through　experiments.　Based　on　the　results　of　incremental　dynamic　analysis,　fragility　analysis　of　two　SBFO　structures　with　different　outrigger　systems　including　conventional　outrigger,　conventional　damped　outrigger,　and　A-NSDO,　was　provided　to　evaluate　structural　vulnerability　for　different　limit　states　like　serviceable　state,　elastic　state,　plastic　state,　and　collapse　state.　The　inelastic　performances　SBFO　tall　buildings　with　different　outrigger　systems　were　discussed　in　detail,　including　seismic　envelopes,　time　history　results,　response　spectra,　and　hysteretic　responses　of　columns,　braces,　and　the　A-NSDO.　Numerical　results　validated　that　the　proposed　A-NSDO　not　only　took　its　advantage　at　elastic　states　for　SBFO　tall　buildings　but　was　also　beneficial　during　the　inelastic　states.