Abstract: The damper is connected to the building structure by setting braces in engineering, but in order to simplify the analysis, the bracing horizontal stiffness is regarded as infinite, that is, the influence of braces on the random response of energy dissipation structure is not considered. In fact, it is more in line with engineering practice to consider the effect of the braces with finite horizontal stiffness on the response of the energy dissipation isolated structure. To analyze the response of the generalized Maxwell energy dissipation isolated structure considering the influence of the braces under the Hu Yuxian spectrum seismic excitation considering the effect of the braces, a concise analytic solution for solving random seismic response is proposed. The non-classical damping system are composed of the equivalent constitutive relation of the generalized Maxwell damper with braces, the motion equation of the isolated structure and the Hu Yuxian spectral filtering equation. The complex modal method is used to decouple the non-classical damping energy dissipation isolated system, and the Duhamel integral expression of the series response of the energy dissipation isolated system based on white noise excitation are obtained through different response modes. Based on the properties of Dirac function, the energy dissipation isolated system series response covariance is simplified into non-integral expression. According to Wiener-Khinchin relationship between the power spectral density function and its covariance function, the energy dissipation isolation system series response power spectrum and ground acceleration power spectrum are obtained. Based on the definition of spectral moments in random vibration theory, the 0 ~ 2 order spectral moments of energy dissipation isolation system series response are obtained. The example verifies the correctness and efficiency of the proposed method in the bracing system by comparing with the pseudo excitation method, and discusses the influence of different bracing stiffness on damping effect of damper.