High-speed train (HST) communications at millimeter-wave (mmWave) band have received a lot of attention due to their numerous high-data-rate applications enabling smart rail mobility. Accurate and effective channel models are always critical to the HST system design, assessment, and optimization. A distinctive feature of the mmWave HST channel is that it is rapidly time-varying. To depict this feature, a geometry-based multipath model is established for the dominant multipath behavior in delay and Doppler domains. Because of insufficient mmWave HST channel measurement with high mobility, the model is developed by a measurementvalidated ray tracing (RT) simulator. Different from conventional models, the temporal evolution of dominant multipath behavior is characterized by its geometry factor that represents the geometrical relationship of the dominant multipath component (MPC) to HST environment. Actually, during each dominant multipath lifetime, its geometry factor is fixed. To statistically model the geometry factor and its lifetime, the dominant MPCs are extracted within each local wide-sense stationary (WSS) region and are tracked over different WSS regions to identify its "birth" and "death" regions. Then, complex attenuation of dominant MPC is jointly modeled by its delay and Doppler shift both which are derived from its geometry factor. Finally, the model implementation is verified by comparison between RT simulated and modeled delay and Doppler spreads.