The damper is connected to the structure by setting the braces, but in order to simplify the analysis, the bracing stiffness is regarded as infinite, that is, the influence of braces on the random response of energy dissipation structure is not considered. Therefore, it is necessary to consider the influence of the braces with finite stiffness on the response of the structure. To analyze the response of the generalized Maxwell energy dissipation isolated structure considering the influence of the braces under the Hu Yuxian spectrum excitation, a concise analytic solution is proposed. The non-classical damping system is composed of the equivalent constitutive relation of the generalized Maxwell damper with braces, the structural motion equation and the Hu Yuxian spectral filtering equation. The complex modal method is used to decouple the system, and the Duhamel integral expression of the system series response based on white noise excitation is obtained through different response modes. Based on the properties of Dirac function, the system series response covariance is simplified into non-integral expression. According to Wiener-Khinchin relationship, the system series response power spectrum and ground acceleration power spectrum are obtained. Based on the definition of spectral moments, the 0 ~ 2 order spectral moments of 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.