Considering the uncertainty and the time variation of frequency contents of real seismic excitation, a new versatile stochastic strong ground motion model named general stochastic seismic ground motion (GSSGM) model is presented in this paper. Some essential assumptions for the earthquake process used in this paper are first given. The intensity and energy of the target seismic ground motion are used to determine the model parameters. The frequency contents are demanded to be agreed with the main characteristics of the target ground motions. The GSSGM model is appropriate to simulate the stationary, intensity non-stationary and fully non-stationary stochastic processes. Additionally, a simple non-stationary stochastic seismic response analysis procedure based on the GSSGM model and the pseudo excitation theory is put forward. The presented non-stationary stochastic seismic response analysis procedure is later applied in the seismic response analysis of a real homogeneous earth dam. The non-stationary analysis results display the effects of non-stationarity on the seismic response of the dam and reflect the main phenomena of dynamic embankment-foundation interaction. The results indicate that the GSSGM model and the presented analysis procedure are effective.