<p>An inerter-based nonlinear energy sink (NESI) is employed in this paper to mitigate the vortex-induced vibration (VIV) of the circular cylinder. The primary objective of the present study is to elucidate the influence of the inerter on the dynamic behavior of the coupled cylinder-NES system and to uncover the underlying mechanism through which the inerter contributes to structural vibration suppression. Numerical simulation results demonstrate that the NESI not only has a smaller secondary mass (only one-third that of the traditional NES) but also maintains comparable vibration suppression performance. Furthermore, the impact of introducing the inerter on the energy transfers between the circular cylinder and NES is analyzed from an energy perspective. The results indicate that incorporating an inerter transforms the energy transfer between the primary structure and the NES from a unidirectional and irreversible process into a bidirectional one, thereby enhancing the NES’s energy dissipation capacity per unit time. In addition, the influence of the inerter on the dynamic characteristics of the NES is investigated. It is found that the inerter modifies the connection type between the additional mass of the conventional NES and the main structure, thereby weakening the effect of nonlinear stiffness and consequently extending both the resonance-capture and resonance durations of the coupled cylinder-NESI system. However, the reduced secondary mass allows the frequency and phase of the NESI to be tuned more easily, enabling the coupled system to reach resonance more quickly. Moreover, the rigid connection between the inerter and the secondary mass increases the difficulty of detuning from resonance, thereby further prolonging the resonance duration. It is also observed that the dynamic output mechanism of the inerter not only eliminates the high-frequency oscillations typically observed in conventional NESs but also enables the NESI to exhibit more robust dynamic behavior.</p>