To address the issue of excessive static displacement in traditional Tuned Mass Dampers （TMD） for low-frequency and long-span bridges， this study introduces the implementation of a Tuned Mass Damper Inerter （TMDI） to increase flutter critical wind speed in such structures. This paper presents a TMDI configuration specifically designed for bridge flutter control and， based on a two-dimensional coupled flutter theory， develops the motion differential equation for the bridge-TMDI system， subsequently deriving the coefficient polynomial characteristic equation. Utilizing the Routh–Hurwitz stability criterion， the flutter critical wind speed is determined. A simply supported beam with an ideal planar cross-section serves as a case study to evaluate the efficacy of TMDI in bridge flutter control and to explore the influence of various TMDI parameter settings on flutter control. The findings reveal that TMDI can effectively increase the bridge flutter critical wind speed. Compared with the traditional TMD， the integration of an inerter may have a minor impact on reducing the control effect； however， it can notably decrease the static displacement of the mass block， thus offering great practical value in real-world engineering applications.