The vortex-induced vibration may cause fatigue of a bridge structure, affecting the safety of vehicles and the comfort of pedestrians. Inerter is a two-terminal device, which has been applied in many areas. This paper studies the problem of suppressing the vortex-induced vibration of a bridge by using an inerter-based dynamic vibration absorber (IDVA). The performances in terms of the suspension travel and the vertical displacement of the bridge with different IDVAs in suppressing vortex-induced vibration are compared, and the effect of the installation position of IDVA on the performance of suppressing vortex-induced vibration is shown. The performance indexes for the vertical displacement of six IDVA arrangements are obtained by using an iterative method, where the performance indexes for the vertical displacement are minimized by using the optimization toolbox in a commercial software. The result shows that the optimal installation positions and the number of suitable installation positions are affected by the resonant mode. Among the six arrangements, one arrangement is identified to have the best performance of suppressing vortex-induced vibration. All the six arrangements have reduced the suspension travel performance.