Ground-anchored suspension bridge owns a neat structure as well as can use the stiff rock condition at the ends of the bridge to share the forces. While under the effects of earthquake motion， the large longitudinal displacement of the girder poses great threat on the safety and serviceability of the bridge. By the way of nonlinear time-history analysis， this paper emphasizes the effect of hydraulic viscous damper on the seismic reduction of ground-anchored Suspension Bridge with single tower and the damper parameter analysis based on Tongmai Bridge. The study indicates that the hydraulic viscous damper can effectively control the longitudinal displacement of the girder. And when the damping index coefficient a remains constant， the longitudinal displacement of the girder decreases with the increase of the damping coefficient C， but the decreasing magnitude is small. On the other hand， the variations of the coefficients of the hydraulic damper have little influence on the forces of critical sections of the tower and foundation.