Inertia and lever components are both force amplification elements in essence，and show excellent performance in the field of vibration control. In order to improve the vibration mitigation performance，two new vibration systems with amplifying mechanisms based on ISD（Inerter-Spring-Damper）structure are designed，and the vibration mitigation effects are studied in detail when the models are subjected to external excitation. Firstly，the dynamic equations are established according to Newton's second law and the analytical solutions of the systems are obtained. It is found that there always exist fixed points independent of the damping ratio in the normalized amplitude-frequency curves. The optimal parameters are respectively obtained based on the H_∞ and H₂ criteria. In addition，the influences of the inerter-to-mass ratio and amplification ratio on the vibration performances are studied. It could be found that the peak values of amplitude-frequency curves are reduced and the distance between two resonance frequencies is broadened when the inerter-to-mass ratio and amplification ratio are increased within a certain range. The correctness of the analytical results is verified by the comparison with numerical simulation. Compared with other systems under harmonic and random excitations，the results show that the presented vibration mitigation systems can greatly reduce the resonance amplitude and broaden the frequency band，and have much better vibration performance.