In order to explore the elastic wave propagation pattern in the ballastless track structure on the periodic bridge, the ballastless track-bridge coupling structure is considered as a four-layers Timoshenko beam coupling model including rail, slab, bed plate and bridge. The plane wave expansion method-energy method was used to solve its dispersion characteristics. The accuracy of the proposed method was verified by comparing with the results of the finite element method. Then, based on this method, the influence of structural stiffness change on elastic wave propagation was explored, and the formation mechanism of band gap in the dispersion characteristics was clarified. The results show that there are two band gaps in the ballastless track-bridge coupling structure within 0~50 Hz, and when the longitudinal stiffness is large, the initial frequency and cut-off frequency are mainly affected by the longitudinal stiffness of each connecting layer. The first and second cut-off frequencies increase with the increase of the stiffness of the glide lamella and the stiffness of the fastener, respectively. This study provides a theoretical reference for the vibration reduction of the ballastless track structure on the bridge.