The periodic characteristics of the track structure have filtering characteristics for the propagation of vibration waves within the structure, and dispersion analysis is important for understanding the vibration transmission characteristics of the track structure. Based on the virtual spring model and the energy functional variation principle, we propose a new method to calculate the complex dispersion of the periodic structure of the rail based on the virtual spring model and the energy functional variation principle, which can consider the damping factor and the material frequency variation effect. The accuracy of the method is verified by comparing with the existing literature, and the method is used to analyze the influence law of fastener stiffness frequency variation effect, fastener damping and ballast damping on the vibration wave complex dispersion characteristics of track structure. The results show that the stiffness frequency variation effect and the fastener and ballast damping have a large influence on the attenuation domain and the attenuation speed of the vibration, which must be considered in the vibration transmission analysis of the track structure.