Tuned　mass　damper　inerter　(TMDI)　has　become　a　popular　choice　for　vibration　control　in　flexible　structures,　including　long-span　bridges,　due　to　its　superior　performance　compared　to　traditional　tuned　mass　dampers　(TMDs),　such　as　improved　control　effect　and　smaller　static　displacement.　However,　the　control　effect　of　TMDI　is　heavily　reliant　on　the　spanning　distance　of　inerter,　which　typically　generates　a　significant　internal　additional　moment　due　to　the　force　imbalance,　limiting　the　practical　application　of　TMDI　on　flexible　structures.　For　this　reason,　a　novel　lever-arm　TMDI　(LTMDI)　is　proposed　in　this　study,　to　suppress　the　vibrations　of　long-span　bridges.　The　non-dimensional　governing　equations　of　the　bridge-LTMDI　system　are　established　in　modal　coordinates,　and　the　closed-form　solutions　of　the　optimum　frequency　and　damping　ratios　of　LTMDI　are　derived　based　on　the　classical　fixed-point　theory.　Parametric　studies　are　conducted　to　investigate　the　influences　of　the　fulcrum　position,　modal　shape　ratio,　mass　ratio,　inertance　ratio　and　asymmetric　mode　on　the　control　effectiveness.　Moreover,　for　comparison,　the　control　effectiveness　of　LTMDI　is　further　compared　to　those　of　the　TMD　and　TMDI.　Finally,　a　long-span　bridge　is　selected　as　an　example　to　demonstrate　the　effectiveness　of　LTMDI　in　reducing　vortex-induced　vibration　(VIV).　The　results　show　that　the　LTMDI　has　superior　control　effect　and　space　feasibility　as　compared　to　the　TMD　and　TMDI　in　both　frequency　and　time　domains.　The　derived　analytical　formulas　can　accurately　determine　the　optimal　parameters,　providing　a　simple　yet　efficient　guideline　for　the　application　of　LTMDI　in　flexible　structures.　©　2023　Elsevier　Ltd