In order to study the application effect of eddy current damper in the field of seismic reduction of super-wide single-rib tied arch bridge， the longitudinal and transverse eddy current dampers are set at the active bearing position of the girder of a new composite structure system of a flexible single rib tied arch bridge with backstays on an ultra-wide bridge deck， respectively. The nonlinear time history analysis method is used to calculate the motion response of the structure under earthquake. In order to facilitate the calculation and application of the eddy current damper， the damping force model was simplified， and the validity of the simplified model was verified by experiments. Finally， the relative displacement between the pier and girder， and the internal force of the arch feet are taken as the evaluation indexes to study the influence of viriable eddy current damper parameters on the seismic response of the structure. The results show that the out-of-plane stiffness of the structure system is low， and it is prone to lateral overturning under earthquake. The structure has high requirements on the bearing capacity of the arch foot. The double broken line model can be approximately equivalent to the nonlinear damping force model of eddy current dampers， which is used to describe the mechanical properties of the eddy current damper . The installation of eddy current dampers can effectively reduce the dynamic response of the bridge structure under earthquake. When the maximum damping force of the damper is determined， the seismic motion response of the structure shows a significant downward trend with the increase of the equivalent damping coefficient. The speed of decline is fast first and then slow， and finally tends to a level after the damping coefficient reaches a certain threshold. The maximum damping force parameter determines the upper limit of the damping force of the eddy current damper. When the equivalent damping coefficient is constant， the motion response of each node of the structure continues to decrease with the increase of the maximum damping force within a certain range.