Based on the power spectral model of filtered Gaussian white noise which is in the stationary earthquake process, the parametric model of fully non-stationary time-varying power spectrum is developed for describing time-varying spectral energy, and a model parameter with engineering significance is obtained through parameter identification. Firstly, the use of bedrock filter to modify the K-T spectrummakes the time-varying spectral parameters have a clear physical meaning and which is more consistent with the physical characteristics of the bedrock ground motion. Furthermore, the time-frequency distribution of the seismic is acquired on account of the generalized harmonic wavelet transform, and the time-varying power spectrum of the actual ground motion is estimated by the Spanos-Tratsk as method. At last, genetic algorithms and second optimization technology are introduced to fit mathematical expressions of time-varying parameters, and a fully non-stationary time-varying power spectral model of ground motion is established. The Japanese KIK-net strong earthquake database is adopted to identify the model parameters, which is reclassified according to the site category in China. Finally, the validity and applicability of the model are verified by the spectral representation method. The ground motion random model proposed in this paper provides a more accurately reference for describing the earthquake, and also provides a basis for the simulation of fully non-stationary ground motion.