The　undesirable　vortex-induced　vibration　(VIV)　may　seriously　influence　the　fatigue　life　and　serviceability　of　bridge　structures.　It　is　important　to　take　countermeasures　to　suppress　the　adverse　VIV　of　long-span　bridges.　In　the　present　study,　a　novel　inerter-based　system,　namely　the　tuned　mass　damper　inerter　(TMDI),　is　proposed　to　control　the　VIV　of　the　main　deck　of　long-span　bridges.　In　this　system,　an　inerter　device,　which　is　able　to　transform　the　linear　motion　into　the　high-speed　rotational　motion　and　thus　significantly　amplifies　the　physical　mass　of　the　system,　is　incorporated　into　the　conventional　tuned　mass　damper　(TMD)　system　to　further　improve　the　performance　of　TMD.　An　applicable　layout　of　the　TMDI　inside　the　bridge　deck　is　introduced　and　the　governing　equations　of　the　structure-TMDI　system　subjected　to　VIV　are　established.　The　optimization　of　the　TMDI　parameters　with　the　consideration　of　nonlinear　aeroelastic　effect　is　derived.　The　control　performance　and　robustness　of　the　proposed　system　are　investigated　through　an　analytical　case　study　in　both　the　time　and　frequency　domains.　It　is　observed　that　the　TMDI　system　can　obviously　reduce　the　VIV　responses　of　the　bridge　deck.　Moreover,　compared　to　the　conventional　TMD　system,　the　static　stretching　of　the　spring　due　to　gravity　and　the　oscillation　amplitude　of　the　mass　block　in　the　TMDI　system　are　significantly　reduced.　These　properties　make　the　proposed　TMDI　system　an　attractive　alternative　for　the　VIV　control　of　long-span　bridges.