Vortex-induced　vibration　(VIV)　of　long-span　bridges　is　frequently　observed　in　various　types　of　bridges　at　low　or　medium　wind　speeds,　causing　disruption　of　traffic,　fatigue　issues　of　the　bridge,　and　even　panic　in　society.　This　study　compares　the　VIV　mitigation　performance　of　the　conventional　tuned　mass　damper　(TMD)　and　three　novel　damping　devices,　i.e.　the　negative-stiffness　damper　(NSD),　inerter-based　damper　(IBD),　and　nonlinear　energy　sink　(NES).　The　governing　motion　equations　of　four　damper-bridge　systems　are　established,　and　the　optimal　parameters　of　each　damper　are　obtained.　The　semi-analytical　solutions　of　controlled　responses　in　the　frequency　domain　are　derived　using　the　harmonic　balance　method　(HBM).　These　four　dampers　are　applied　to　mitigate　the　VIV　of　a　parallel　box　girder　bridge,　which　was　observed　and　studied　in　the　wind　tunnel　tests.　Their　performance　is　examined　using　semi-analytical　solutions　in　the　frequency　domain　and　numerical　solutions　in　the　time　domain　based　on　the　Runge-Kutta　method,　respectively.　The　control　efficiency,　the　stroke　of　the　auxiliary　block,　and　the　robustness　of　these　four　systems　are　compared.　The　strengths　and　weaknesses　of　different　dampers　used　for　VIV　mitigation　in　bridge　girders　are　discussed.　The　findings　of　this　study　provide　the　basis　for　determining　the　most　favorable　damper　devices　for　VIV　mitigation　to　adapt　the　specific　requirements　of　different　bridges.