Abstract: Considering the complexity of solving the seismic response of the energy-dissipated isolated structure with six-parameter viscoelastic damper under the excitation of Li Hongjing spectrum， a concise solution that can obtain random seismic response is pro? posed. The analysis model of six-parameter viscoelastic damper with support is adopted， and the mathematical modeling of energy dissipation and isolation structure with viscoelastic damper is realized by differential constitutive equation. Combined with complex mode method and the pseudo excitation method （PEM）， the unified expression of frequency domain solution for system series re? sponse （displacement， velocity and damper force） of vibration isolation system is obtained. Taking Li Hongjing spectrum as the ex? citation power spectrum， the excitation power spectrum and the eigenvalue function of structural frequency response are simplified， and the concise analytical solutions of the system response power spectrum， response spectral moment and response variance under the random excitation are obtained. An example is given to verify the accuracy and efficiency of the proposed method in analyzing the dynamic response of the system compared with the traditional response analysis method such as the PEM， and the influence of different support stiffness on the vibration reduction effect of the damper is discussed.