A vibration damping apparatus including reference wave production section that produces a reference wave; a fundamental order adaptive algorithm block that calculates fundamental order adaptive filter factors from a vibration detection signal and the reference wave and produces a fundamental order vibration damping current instruction; an amplitude detection section that calculates a peak current value of the fundamental order vibration damping current instruction; and a fundamental order current excess detection section that derives a fundamental order current upper limit value from the fundamental frequency to produce a fundamental order current upper limit excess signal that is output to the fundamental order adaptive algorithm block, which revises the fundamental order adaptive filter factors in a direction in which the vibration damping current instruction is limited within a range.