In order to explore the elastic wave propagation law in the ballastless track structure on the periodic bridge, the ballastless track-bridge coupling structure is considered as a four-layer Timoshenko beam coupling model including rail, track plate, base plate and bridge. The plane wave series expansion method-energy method is used to solve its dispersion characteristics. The accuracy of the proposed method is verified by comparing with the finite element simulation results. Then, based on this method, the influence of structural stiffness change on elastic wave propagation is explored, and the formation mechanism of band gap in dispersion characteristics is clarified. The results show that there are two forbidden bands in the structure within 0-50 Hz, and 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 glide lamella stiffness and fastener layer stiffness respectively. The research provides a theoretical reference for the vibration reduction of ballastless track structure on bridge.