The invention provides a shock-absorbing damper. The shock-absorbing damper comprises a cylindrical shell, a piston rod penetrating through the upper base of the cylindrical shell, at least two damping units arranged between the piston rod and the cylindrical shell and disc springs arranged between the damping units. The uppermost damping unit is connected with the upper base of the cylindrical shell through a fixing piece, and the lowest damping unit is connected with the lower base of the cylindrical shell through a fixing piece. The piston rod is sleeved with locking nuts. The locking nutsare arranged on the upper side of the uppermost damping unit and on the lower side of the lowest damping unit correspondingly. The shock-absorbing damper can absorb much kinetic energy generated by anearthquake, reduces dynamic response of equipment to the earthquake, effectively protects the equipment and improves the equipment installation reliability and use stability; the disc springs have the resetting function, so that the shock-absorbing damper can recover to the initial position after the earthquake, and the shock-absorbing damper is convenient and easy to use and good in damping effect.