A damping device includes a calculator calculating a pseudo vibration to cancel a source vibration transmitted from a vibration source to a position to be damped, using an adaptive control algorithm. The canceling vibration is generated according to the pseudo vibration. A vibration detector detects an error vibration remaining at the position. The adaptive control algorithm is adapted by learning to reduce the error vibration. A frequency recognizer recognizes a frequency of the source vibration from a signal related to the vibration source. The frequency of the vibration is used to determine a frequency of the pseudo vibration. A phase difference identifier identifies a phase difference between the error vibration and the canceling vibration according to the pseudo vibration, and a frequency corrector corrects, according to the phase difference, the frequency of the vibration to eliminate the phase difference.