Abstract: This study proposes a vibration control scheme for suppressing the vibration of a fluid-conveying pipe with elastically constraints using an inerter-based nonlinear energy sink (INES). The governing equations of the system are derived based on the generalized Hamilton’s principle. The assumed mode method is utilized to determine the modal properties of the coupled system. To derive an approximate analytical solution, the harmonic balance method is employed to solve the equations after they have been truncated by the Galerkin method. The accuracy of the results obtained from the harmonic balance method is verified by comparison with the fourth-order Runge-Kutta method. The key parameters of the INES, such as its inerter coefficient, nonlinear stiffness, and damping, are systematically analyzed for their effect on vibration control. The results indicate that as the inerter coefficient and nonlinear stiffness of the INES gradually increase, the first-order resonance peak of the system decreases. When the damping of the INES increases, the first-order resonance peak of the system first decreases and then increases. However, compared to the original system, the amplitude of the resonance peak is significantly reduced across all different damping values. The effect of simultaneously varying the nonlinear stiffness and damping of the INES on vibration reduction efficiency is also analyzed, revealing that there exists an optimal parameter range for the INES. The effect of fluid speed on pipe vibration is analyzed. It is found that as the fluid speed increases, the first-order resonance peak of the pipe gradually intensifies and shifts to the left. Finally, the effects of the position of the INES on the pipe vibration is analyzed. It is found that the optimal installation position of the INESs is determined by the modal shape of the pipe. The INES achieves the best performance when installed at the location of the maximum modal displacement. The proposed INES-based vibration control scheme for the pipe system achieves high-efficiency vibration control with minimal added mass, providing theoretical guidance and technical reference for the engineering practice of vibration control in fluid-conveying pipes.