In order to explore the effect of hysteresis damping on the band gap of periodic track structure, the ballast track of our country was taken as an example, and the band gap characteristics were analyzed based on the energy functional variational principle. By introducing hysteretic damping effect into rails, fasteners and track bed, the variation of dispersion characteristics with damping of periodic ballasted track is studied. Furthermore, the vibration transmission characteristics of the track structure under the effect of damping are studied. The results show that the band gap range of the undamped track structure is consistent with the attenuation range of the vibration response; the rail damping is very small and has little effect on the band gap of the track structure, which can be ignored when calculating and predicting vibration; the damping of the fasteners will slightly increase the track structural band gap and has little effect on the overall band gap, but for the vibration response, the dissipation effect of the fastener damping will increase the vibration attenuation range within 150Hz~500Hz; the increase of the ballast bed damping will increase the first-order band gap range, but it will decrease the second-order bandgap range, in the vibration response, increasing the damping of the track bed can dampen the vibration of the rail within 260 Hz.