Bridge cables should always be equipped with vibration mitigation measures and monitoring techniques. The proposed electromagnetic damper was developed to reduce vibration of the cable and utilize induction current as the power source of the wireless sensor. Major parameters for the design of the damper were derived. Then, the cable experiment was carried out under the conditions of free vibration and force vibration. For free vibration conditions, the change of damping ratio according to the acceleration amplitude evaluation point was analyzed through Hilbert transform. As a result, the damping performance of the passive electronic damper applying the external resistance under the free vibration condition was improved to 2.18% of the maximum damping ratio and 1.88% of the average damping ratio. Under the sinusoidal forced vibration conditions, it was found that the acceleration and frequency domain response at each measurement point of the cable decreased by 30% to 50% or more, and the RMS displacement response decreased by 45% to 49% under the excitation with 1st to 3rd natural frequencies. In addition, it has been confirmed that effective damping performance is exhibited in the 2nd and 3rd natural frequency, which are the main response conditions of the cable. Hybrid simulation was carried out to evaluate the energy harvesting performance of the electromagnetic damper. As a result, the output power was 174.6mWh at the mean wind speed of 5.4 m/s. Even if the sensor and the battery loss were considered, enough power was generated to operate the wireless sensor.