An object of the invention is to provide a vibration damping system that can avoid the occurrence of resonance of an elevator rope regardless of the vibration frequency of a vibration source. A vibration damping system (200) includes a displacement amplifier (7), a calculation unit (66), and a displacement amplification control unit (67). The displacement amplifier (7) is arranged along a given position in the longitudinal direction of the elevator rope. The displacement amplifier (7) amplifies a displacement due to vibration of the elevator rope based on a variable amplification factor. The calculation unit (66) calculates the natural frequency of the elevator rope. The displacement amplification control unit (67) controls the displacement amplification of the displacement amplifier (7) based on the natural frequency calculated by the calculation unit (66) and a preset vibration frequency.