Stochastic simulation of spatially distributed ground‐motion time histories is important for performance‐based earthquake design of geographically distributed systems. In this study, we develop a novel technique to stochastically simulate regionalized ground‐motion time histories by taking account of the influence of regional site conditions. For this purpose, a transient acceleration time history is characterized by wavelet‐packet parameters proposed by Yamamoto and Baker (2013). The wavelet‐packet parameters can fully characterize ground‐motion time histories in terms of energy content, time–frequency‐domain characteristics and time–frequency nonstationarity. This study further investigates the spatial cross correlations of wavelet‐packet parameters based on geostatistical analysis of 1500 regionalized ground‐motion data from eight well‐recorded earthquakes in California, Mexico, Japan, and Taiwan. The linear model of coregionalization (LMC) is used to develop a permissible spatial cross‐correlation model for each parameter group. The geostatistical analysis of ground‐motion data from different regions reveals significant dependence of the LMC structure on regional site conditions, which can be characterized by the correlation range of VS30 in each region. In general, the spatial correlation and cross correlation of wavelet‐packet parameters are stronger if the site condition is more homogeneous. The proposed region‐specific correlation model improves stochastic simulation of spatially correlated ground motions, as is demonstrated in illustrative examples in this article. The developed method has great potential to be used in computationally based seismic analysis and loss estimation in a regional scale.