The invention belongs to the technical field of engineering structure control, and in particular relates to a stayed cable vibration damper and a design method for an apparent mass rotating electromagnetic damper. The stayed cable vibration damper comprises a damping device and a transmission mechanism, the transmission mechanism is used for connecting the stayed cable and the damping device, the design method comprises the steps that the fundamental frequency of the stayed cable is determined; the installation location of the apparent mass rotating electromagnetic damper is determined; the damping parameters of the apparent mass rotating electromagnetic damper is calculated; and the stiffness parameters of the apparent mass rotating electromagnetic damper is calculated. According to the stayed cable vibration damper and the design method for the apparent mass rotating electromagnetic damper, a ball screw is utilized to effectively improve the rotational speed of the rotating electromagnetic damper, the equivalent damping coefficient of the damper is improved, and the energy consumption efficiency of the electromagnetic damper is improved; and an inertia flywheel mounted on a rotating shaft of the electromagnetic damper generates an apparent mass effect, the apparent mass effect is amplified through a ball screw mechanism, the stayed cable vibration damping mechanism is provided passive negative stiffness control characteristics, and the vibration damping effect of the stayed cable is effectively improved.