Tuned　mass　damper　inerter　(TMDI)　is　a　promising　device　for　structural　vibration　control.　Existing　design　formulas　for　TMDI　are　derived　based　on　an　undamped　single-degree-of-freedom　primary　structure.　When　applied　to　vortex-induced　vibration　(VIV)　control　of　bridges,　it　may　lead　to　a　suboptimal　design　of　TMDI,　since　VIV　is　characterized　by　nonlinear　aeroelastic　effect　and　sensitive　to　the　structural　damping.　This　study　proposes　closed-form　design　formulas　of　TMDI　that　are　suitable　for　VIV　control　of　bridges.　Governing　equations　of　the　bridge-TMDI　system　are　first　established　in　modal　coordinate.　Based　on　these　equations,　the　equivalent　damping　of　TMDI　to　the　bridge　is　derived.　Then,　the　design　formulas　for　TMDI　frequency　and　damping　ratio　with　predetermined　TMDI　mass,　inertance,　and　inerter　arrangement　are　developed　to　achieve　the　required　equivalent　damping　of　TMDI.　The　reliability　of　the　proposed　formulas　is　validated　by　utilizing　the　wind　tunnel　experimental　data　of　a　bridge.　It　is　found　that　the　effect　of　TMDI　to　the　bridge　can　be　treated　as　an　increase　of　the　structural　damping.　It　is　also　found　that　the　TMDI　parameters　will　betray　the　optimum　values　if　the　VIV　force　model　fails　to　correctly　predict　the　required　equivalent　damping　of　TMDI.　To　eliminate　this　disadvantage,　some　design　suggestions　are　presented.　The　comparison　with　existing　TMDI　design　formulas　and　discussions　on　the　application　scope　of　the　proposed　formulas　are　also　conducted.　The　proposed　formulas　can　achieve　a　better　control　efficiency　for　the　same　predetermined　TMDI　parameters　and　have　high　accuracy　within　the　scope　of　practical　engineering　applications.