Previous　studies　have　shown　superior　control　performance　in　mitigating　vibrations　of　stay　cables　by　using　passive　control　devices　such　as　negative　stiffness　dampers　(NSDs)　and　inertial　mass　dampers　(IMDs).　Integrating　the　advantages　of　the　two　dampers,　we　propose　a　novel　passive　control　device　termed　magnetic　negative　stiffness　eddy-current　inertial　mass　damper　(MNS-ECIMD)　for　cable　vibration　mitigation.　A　mechanical　model　of　the　MNS-ECIMD　is　proposed　and　validated　against　dynamic　test　data　of　a　small-scale　prototype.　A　parametric　analysis　is　conducted　based　on　the　finite　difference　model　of　the　cable-damper　system　to　investigate　the　effects　of　the　magnetic　negative　stiffness　coefficient,　inertance　coefficient,　and　eddy-current　damping　coeffi-cient　of　the　MNS-ECIMD　on　cable　vibration　mitigation　performance.　The　MNS-ECIMD　perfor-mance　is　further　validated　using　a　small-scale　cable　test,　of　which　the　results　illustrate　its　superior　performance　for　the　first　two　modes　compared　with　the　ECIMD.　A　simple　parameter　optimization　procedure　is　then　presented　for　cable　multi-mode　vibration　control,　which　is　then　demonstrated　via　numerical　simulation　of　a　306　m-long　stay　cable　of　Stonecutter　Bridge　in　Hong　Kong.　Nu-merical　results　illustrate　that　the　MNS-ECIMD　significantly　outperforms　conventional　viscous　dampers　and　the　ECIMD　for　cable　multi-mode　vibration　control,　owing　to　the　additional　negative　stiffness　effect.