An inerter is introduced in the traditional nonlinear energy sink (NES) to replace its mass and constitutes the novel inerter-based nonlinear energy sink (INES). The INES combines the mass amplification effect of the inerter and the vibration dissipation effect of the NES, which satisfies the lightweight design requirement and further mitigates the vibration of the main structure. Here, the INES is applied in the half-vehicle system to investigate its dynamic performance both in the vertical and pitching directions. The dynamic model of the half-vehicle system coupled with INES is established, the harmonic balance method (HBM) and pseudo arc length method (PALM) is used to obtain its dynamic response under road harmonic excitation. The corresponding dynamic performance under road harmonic and shock excitations is evaluated using six performance indices, which considers the vertical and pitching vibrations of the vehicle body, suspension deflection, and road holding; the vibration suppression effect of the INES and traditional NES is compared. The results show that the traditional NES can enhance the dynamic performance of the half-vehicle system slightly at the cost of a very large mass, which violates the vehicles’ lightweight design and cannot be realized in the practical engineering. For road harmonic excitation, using the INES can obtain a better dynamic performance for the front and rear suspension deflections, front and rear dynamic tire loads, vehicle body vertical acceleration in high vehicle velocity, while the vehicle body pitching acceleration is larger. For road shock excitation, applying the INES can improve the shock performance for the front and rear suspension deflections, front and rear dynamic tire loads, while the peak values of the vehicle body vertical and pitching accelerations are larger. Therefore, the INES integrates the benefits of the inerter and NES and provides a new vibration attenuation device design in the vehicle engineering.