Spatially variable ground motions are crucial for the seismic analysis and design of extended and multi-support structures. In this study, a new random nonstationary spatially variable ground motion model based on the propagation process of seismic waves is proposed. In particular, the amplitude and phase transfer functions of seismic waves at the local site are studied herein. The probability density function of the corresponding parameters is given. Two simple examples are used to show the generation of random ground motions. Compared with traditional methods, our proposed model not only has a clear physical background but also shows good practicability. The model should be for those researchers who want to use nonstationary spatially variable ground motions to study the seismic response of lifeline systems or building portfolios.