In time-variant high-speed train (HST) radio channels, the scattering environment changes rapidly with the movement of terminals, leading to a serious deterioration in communication quality. In the system-and link-level simulation of HST channels, this non-stationarity should be characterized and modeled properly. In this paper, the sizes of the quasistationary regions are quantified to measure the significant changes in channel statistics, namely, the average power delay profile (APDP) and correlation matrix distance (CMD), based on a measurement campaign conducted at 2.4 GHz. Furthermore, parameters of the multi-path components (MPCs) are estimated and a novel clustering-tracking-identifying algorithm is designed to separate MPCs into line-of-sight (LOS), periodic reflecting clusters (PRCs) from power supply pillars along the railway, and random scattering clusters (RSCs). Then, a non-stationary geometry-cluster-based stochastic model is proposed for viaduct and hilly terrain scenarios. Furthermore, the proposed model is verified by measured channel statistics such as the Rician K factor and the root mean square delay spread. The temporal autocorrelation function and the spatial cross-correlation function are presented. Quasi-stationary regions of the model are analyzed and compared with the measured data, the standardized IMT-Advanced (IMT-A) channel model, and a published nonstationary IMT-A channel model. The good agreement between the proposed model and the measured data demonstrates the ability of the model to characterize the non-stationary features of propagation environments in HST scenarios.