A new stochastic ground motion model for generating a suite of ground motion time history with both temporal and frequency nonstationarities for specified earthquake and site characteristics is proposed based on the wavelet method. This new model is defined in terms of 6 key parameters that characterize the duration, evolving intensity, predominant frequency, bandwidth and frequency variation of the ground acceleration process. All parameters, except for peak ground acceleration (PGA), are identified manually from a database of 2444 recorded horizontal accelerations. The two-stage regression analysis method is used to investigate the inter- and intra-event residuals. For any given earthquake and site characteristics in terms of the fault mechanism, moment magnitude, Joyner and Boore distance and site shear-wave velocity, sets of the model parameters are generated and used, in turn, by the stochastic model to generate strong ground motion accelerograms, which can capture and properly embody the primary features of real strong ground motions, including the duration, evolving intensity, spectral content, frequency variation and peak values. In addition, it is shown that the characteristics of the simulated and observed response spectra are similar, and the amplitude of the simulated response spectra are in line with the predicted values from the published seismic ground motion prediction equations (SGMPE) after a systematic comparison. The proposed method can be used to estimate the strong ground motions as inputs for structural seismic dynamic analysis in engineering practice in conjunction with or instead of recorded ground motions.