Inerter-based　dampers　(IBDs)　have　been　proposed　to　enhance　the　efficiency　of　conventional　tuned　mass　dampers　(TMDs)　in　controlling　wind-induced　vibration　of　civil　structures　recently.　In　this　paper,　four　different　IBDs,　with　each　featuring　a　specific　combination　of　dashpot-spring　elements　in　series　or　in　parallel　with　the　inerter　device,　are　applied　to　control　the　vortex-induced　vibration　(VIV)　of　long-span　bridges.　The　governing　equations　of　the　bridge-IBD　system　under　the　effect　of　VIV　are　established,　and　the　strategy　to　optimize　the　IBD　parameters　is　proposed.　The　performances　of　different　IBDs　in　terms　of　mitigating　the　VIV　response　of　the　deck,　the　stroke　of　mass　block,　the　static　deformation　of　spring　due　to　gravity,　the　reaction　force　of　IBDs　on　the　bridge　deck,　and　the　robustness　of　the　system　(the　control　efficiency　against　the　deviation　of　design　parameters　from　their　optimal　values)　are　systematically　evaluated　and　compared.　Through　this　comparative　study,　the　superiorities　of　IBDs　to　conventional　TMDs　in　bridge　VIV　control　are　illustrated,　and　two　feasible　layouts　of　IBDs　that　are　suitable　for　bridge　VIV　control　are　suggested.　On　the　basis　of　these　results,　the　guideline　for　VIV-resistance　design　of　long-span　bridges　with　the　help　of　IBDs　is　also　proposed.