With　the　increment　of　cable　length,　long　stay　cables　are　prone　to　experience　high-mode　vortex-induced　vibrations　(VIVs)　at　normal　wind　velocities,　and　the　VIV-prone　mode　range　also　becomes　wider.　Existing　dampers　cannot　supply　sufficient　damping　for　such　a　wide　range　of　high-modes.　Inerter-based　dampers　(IBDs),　which　take　advantage　of　the　two-terminal　inertial　device　dubbed　inerter,　have　been　proved　to　have　a　better　control　performance　than　conventional　dampers.　However,　existing　studies　on　IBDs　only　focused　on　the　first　several　cable　modes,　which　cannot　cover　the　wide　range　of　VIV-prone　modes　of　long　stay　cables.　The　high-mode　and　multi-mode　VIV　control　by　using　IBDs　is　investigated　in　this　study.　The　governing　equations　of　the　cable-IBD　systems　under　VIV　are　first　established.　The　control　efficiency　of　the　IBDs　and　the　influence　of　optimum　design　strategies　are　compared.　The　use　of　two　IBDs　to　further　enhance　the　control　efficiency　is　also　discussed.　The　results　show　that　a　three-element　IBD　in　this　study　is　quite　effective　for　high-mode　and　multi-mode　VIV　control　of　long　stay　cables.　Moreover,　the　multi-mode　control　efficiency　can　be　further　improved　through　using　two　IBDs.　The　results　in　this　study　can　guide　the　design　of　IBDs　for　VIV　control　of　long　stay　cables.