<p>The inertial damper, characterized by its flat potential well, exhibits adaptability to vibrations of any frequency and amplitude. As a continuous system, pipe systems possess numerous resonance frequencies. Consequently, inertial dampers offer the capability for adaptive vibration suppression across multiple resonance modes in pipe systems. In this paper, an inertial damper composed of visco-hyperelastic material is proposed and modeled as a mass-damping system for the first time. The governing equation for the pipe's bending vibration incorporating the inertial damper is established based on Newton's second law and the constitutive relationship model of the visco-hyperelastic material. Subsequently, the complex natural characteristics of the pipe system influenced by the inertial damper are analyzed, where the real part represents the vibration frequency, and the imaginary part signifies energy dissipation. Following this, the vibration response is solved using the harmonic balance method (HBM) and numerically verified by the Runge–Kutta method (R–K). Finally, the material parameters and placement position are discussed to optimize multi-modal vibration control of the pipe system. The findings indicate that the inertial damper made of visco-hyperelastic material has a minor impact on the real natural frequencies of the pipe system but significantly increases the imaginary part. As a result, bending resonance in the pipe is effectively suppressed. The proposed inertial damper provides a simple structural design and theoretical foundation for vibration reduction technology in pipe systems.</p>