In this paper, we propose a new on-line adaptive relaxation algorithm for an inverse filter in a multichannel sound reproduction system. The fluctuation of room transfer functions degrades reproduced sound in conventional sound reproduction systems in which the coefficients of the inverse filter are fixed. In order to resolve this problem, an iterative relaxation algorithm for an inverse filter performed by truncated singular value decomposition (adaptive TSVD) has been proposed. However, it is difficult to apply this method within the time duration of the sound of speech or music in the original signals. Therefore, we extend adaptive TSVD to an on-line-type algorithm based on the observed signal at only one control point, normalizing the observed signal with the original sound. The result of the simulation using real environmental data reveals that the proposed method can always carry out the relaxation process against acoustic fluctuation, for any time duration. Also, subjective evaluation in the real acoustic environment indicates that the sound quality improves without degrading the localization.