The invention relates to a bridge trunnion base with a damping device, which belongs to the field of shock absorbing technology of a cutter-suction dredger. The bridge trunnion base comprises a bridge trunnion, a first shaft sleeve, a trunnion sleeve, a second shaft sleeve, a bridge trunnion base and a plurality of circular arc connecting plates, wherein the circular arc connecting plates are uniformly distributed at the inner edge of the bridge trunnion base and the outer edge of the trunnion sleeve in the radius direction; the first shaft sleeve and the second shaft sleeve are arranged on the inner side of the trunnion sleeve from outside to inside in sequence; one end of the bridge trunnion is fixedly arranged on the inner side of the second shaft sleeve; and the other end of the bridge trunnion is connected with the bridge. After the damping device is installed, the maximum vibration amplitude value transferred to the dredger body is reduced by 20 percent, therefore, the bridge trunnion base with the damping device can effectively reduce the vibration of the bridge transferred to the dredger body structure, and the aim of reducing the vibration of the dredger body is achieved.