Inerter-based　dynamic　vibration　absorbers　(IDVAs)　have　been　theoretically　studied　in　the　vibration　control　of　civil　structures.　However,　experimental　studies,　especially　studies　on　the　nonlinearity　of　this　mechanical　device　and　its　influence　on　the　control　efficiency　of　civil　structures,　are　limited.　In　the　present　study,　a　ball-screw　inerter　aimed　to　control　the　vortex-induced　vibration　(VIV)　of　a　scaled　bridge　model　is　designed　and　manufactured.　The　dynamic　property　of　this　device　is　examined　through　experiments.　A　nonlinear　physical　model　is　proposed　to　simulate　this　device　and　is　incorporated　into　the　governing　equations　of　the　bridge-TMDI　(tuned　mass　damper　inerter)　system　to　investigate　its　influence　on　VIV　control　efficiency.　Design　suggestions　on　how　to　mitigate　the　influence　of　inerter　nonlinearity　are　also　proposed.　The　results　indicate　that　the　dynamic　property　of　the　ball-screw　inerter　depends　on　the　magnitude　of　driving　acceleration.　With　the　increment　of　acceleration　magnitude,　the　ball-screw　inerter　approaches　an　ideal　linear　inerter.　Due　to　this　acceleration-dependent　property,　the　control　efficiency　of　the　TMDI　when　considering　the　inerter　nonlinearity　is　worse　than　that　of　an　ideal　linear　TMDI.　By　retuning　the　optimum　design　parameters　of　a　TMDI　obtained　based　on　linear　assumption,　the　influence　of　inerter　nonlinearity　can　be　compensated　to　some　extent.　In　addition,　for　a　certain　designed　inertance,　one　can　choose　a　larger　diameter　of　a　ball　screw　and　a　larger　value　of　lead　to　further　reduce　the　influence　of　inerter　nonlinearity.　Even　though　this　design　option　will　reduce　the　mass　amplification　ratio　of　the　inerter,　the　actual　physical　mass　of　the　inerter　is　still　ignorable　as　compared　with　the　mass　of　the　TMDI　mass　block.