Tuned　mass　damper　inerter　(TMDI)　has　been　proved　to　be　a　feasible　device　for　vibration　control　of　long-span　bridges　due　to　its　excellent　space　performance.　However,　existing　design　method　for　TMDI　is　conducted　mode-by-mode.　When　applied　to　multi-mode　control　of　the　bridge　through　multiple　TMDIs,　it　cannot　consider　the　synergistic　effect　among　the　TMDIs　and　thus　leading　to　a　suboptimum　design　result.　This　paper　presents　an　efficient　method　for　multi-mode　vortex-induced　vibration　(VIV)　control　of　long-span　bridges　by　using　spatially　distributed　TMDIs　(DTMDIs).　The　governing　equations　of　the　bridge-DTMDIs　system　are　established　in　modal　coordinate.　A　global　optimization　method　considering　the　synergistic　effect　among　the　DTMDIs　is　proposed　and　compared　with　conventional　mode-by-mode　approach　through　a　numerical　case　study.　The　robustness　of　the　control　schemes　against　variations　in　structural　and　aerodynamic　parameters　is　investigated.　The　influence　of　inerter　span　length　on　the　control　efficiency　is　also　discussed.　The　results　show　that　the　proposed　global　design　method　can　achieve　a　better　control　efficiency　with　even　less　TMDIs　as　compared　with　conventional　mode-by-mode　approach.　The　proposed　method　can　also　be　extended　to　VIV　control　of　some　other　line-like　structures.　©　2022　Elsevier　Ltd