Among the power spectrum models of earthquake ground motions, the Clough-Penzien spectrum (C-P spectrum for short) model is more accurate, reliable and clear in physical meaning. However, it requires a large number of identification parameters. On the other hand, the ordinary least squares (OLS) algorithm has the difficulty in selection of initial values for nonlinear identification, as well as the inability to quickly and effectively realize the accurate identification of large-scale parameters. In this paper, the adaptive weighted particle swarm optimization (AWPSO) algorithm is used to identify the parameters of the C-P spectrum model with the typical seismic ground motion records. To this end, 4159 seismic records are selected from the ground motion database, and grouped according to the site classification standards in the Code of Seismic Design of Buildings. The AWPSO algorithm is used to identify the parameters of the C-P spectrum models of various sites. The K-S test and A-D test as well as the AIC and BIC information criteria are employed to determine the optimal probability distribution model for each parameter, the correlation coefficients between each couple of parameters are calculated, and the joint probability density functions of the C-P spectrum model parameters are established. The Latin hypercube sampling method is used to obtain the statistical samples of the C-P spectrum model of each site, which is compared with the power spectrum transformed by the standard code design spectrum. The synthesis method for artificial ground motions with the iterative correction method of the power spectrum is used to generate artificial seismic records with site characteristics. The parameter identification method and the statistical models of the C-P model parameters proposed by this paper can provide an efficient approach and guidance for stochastic simulation and synthesis of earthquake ground motions.