Abstract: The model of a power spectral density function is developed for the stationary stochastic process presenting the earthquake ground motion. First, the acceleration of motion on the rock is assumed to be a random process with characteristic of filtered Gaussian white noise, in which the spectral amplitudes are reduced during both the lower frequency extent and the higher frequency extent by two frequency control parameters. Thus the physical properties of the rock motion are simulated and the energy of the motion is finite. Then the overlaying soil is represented to be a linear single-degree-of-freedom system, and the power spectral density function of the ground acceleration is solved by the random dynamic analysis procedure for the SDOF system, excited by the motion of the rock. Furthermore, the physical mechanism of the modeling presented is explained, and the instrumented data of the strong ground motion received from the 2008 Wenchuan earthquake are employed to fit the parameters in the model for the illustration to the reasonable values of the modeling parameters. It may be considered that the stationary model presented is a modified Kanai-Tajimi spectrum because of the use of the Kanai filter, but eliminates the singular point in zero frequency existed in the Kanai-Tajimi spectrum.