Based on the layout form of damper， spring and inerter， which is applied to the quasi-zero stiffness （QZS） vibration isolator， the parallel-connected and series-connected inerter-based QZS vibration isolators are proposed. The dynamic characteristics of the two inerter-based QZS vibration isolators under harmonic force excitation are studied. Utilizing the harmonic balance method， the dynamic response of the system is obtained. Besides， the influence of two main structural parameters （inertance-to-mass ratio and stiffness ratio） on the dynamic characteristics of the system is revealed and four performance indices， which are peak dynamic displacement， peak force transmissibility， isolation frequency band and force transmissibility， are defined to evaluate the isolation performance of the systemin the high-frequency band. The results show that compared with the QZS vibration isolator， the parallel-connected inerter-based QZS vibration isolator has a smaller peak force transmissibility and a larger isolation frequency band， while the peak dynamic displacement and force transmissibility in the high-frequency band is larger. Moreover， the series-connected inerter-based QZS vibration isolator can widen the isolation frequency band and the force transmissibility in the high-frequency band approaches to zero， while the peak dynamic displacement and peak force transmissibility are larger. Hence， the study provides theoretical guidance for applying the inerter in the QZS low-frequency isolation area.