In this study, a stochastic simulation model proposed by Yamamoto and Baker (2013), is applied to Iranian strong motion database which comprises more than 3828 recordings for a time period between 1975–2018. Each ground motion is decomposed into wavelet packets. Amplitudes of wavelet packets are divided into two groups and for each group model parameters are estimated using the maximum likelihood method. Regression coefficients are then obtained relating model parameters to seismic characteristics such as earthquake magnitude, distance, and site condition. Inter-event residuals of coefficients and correlation of total residuals of those parameters are also calculated. To reconstruct the amplitudes in time domain and do the simulation, inverse wavelet packet transform is used. Finally, a validation test is performed. The comparison of ground motion intensity measures for recorded and simulated time series shows an acceptable conformity in the application. The estimated parameters using the simulated data are in good agreement with the real data, indicating the acceptable validity of the estimated stochastic simulation model. Obtained regression equations can be used to generate ground motions for the future earthquake scenarios in Iran.