The Maxwell model with viscoelastic characteristics was introduced into the system to propose a new dynamic vibration absorber（DVA）with inerter and grounded stiffness，and the system parameters were optimized. The analytical solution was obtained based on the established dynamic equation. Three fixed-points were found in the amplitude-frequency curves. The optimal frequency ratio and optimal stiffness ratio of the DVA were determined by adjusting the three fixed points to the same height according to the fixed points theory，and the optimal damping ratio of the system was also obtained according to H∞ optimization criterion.In the process of parameter optimization，when the inerter ratio was within a certain range，two groups of optimal parameters suitable for the model were found，and then the optimal parameters corresponding to different inerter ratios were determined. Considering the practical engineering application and ensuring the system stability，the optimization results of the two groups of parameters were compared，and the optimal working range of the inerter ratio was determined under the conventional parameters. The influence of the choice of system parameters on the system response inside and outside the optimal working range of inerter ratios was analyzed，and the suggestions in the practical engineering application were given. Compared with the existing dynamic vibration absorbers under harmonic excitation and random excitation，it shows that the system has obvious vibration reduction advantages by selecting the appropriate inerter ratio，which provides a theoretical basis for the design of new dynamic vibration absorbers.