A double-ring shaped strong magnet array nonlinear dynamic vibration absorber for vibration mitigation of suspender cables and design method thereof, which belongs to the field of structural vibration control. The installation positions and number are designed according to the demand of vibration mitigation, and usually one is installed at the midpoint of the suspender cable. The vibration absorber consists of the inner and outer magnet ring arrays, the additional weights, the universal wheels and a base. It feeds back the control force in the opposite direction of the motion of the suspender cable during the movement, so that the vibration energy of the suspender cable is transferred to the vibration absorber and thus less is returned to the suspender cable, and the energy dissipated through the friction between the universal wheels and the base, adding air dampers and other measures, etc.