In this paper, a new type of inertial damper for cables with a combination of rack and pinion, inertial element, and viscous damping element was proposed.A theoretical design method of each element parameter of the damper was given, and the principle of energy consumption was pointed out.By using theoretical derivation combined with a numerical calculation method to give its single energy dissipation performance, the in-plane motion equation of the cable-inertial damper system was established.By using the complex modal analysis method, the cable-inertia considering the sag was given.Formula for calculating the modal damping ratio of a mass damper system was given.For a certain actual cable, by using the dimensionless analysis method, the design parameters of the real cable inertial damper and the corresponding cable modal damping ratio were given.The damping effect of the same inertial damper parameters on different cable vibration modes was studied.The results show that the cable with sag will approach the fixed frequency of this order when the inertia or damping increases.For an actual super-long cable, when the order of the target vibration-damping mode is not too much, after multi-parameter tuning of inertia, viscous damping and installation position, a broad-spectrum damping superior to the existing viscous damper vibration effect can be obtained.