In man-machine communication by speech under the noisy environment, the quality of speech may be degraded severely for the machine to recognize correctly. Especially when the corrupting noise occupies the same band as the speech, the conventional fixed filters cannot filter out the noise effectively. In recent, to resolve such a problem adaptive noise canceller (ANC) is frequently used, which is based upon adaptive filters. The Adaptive recursive filters perform better than adaptive nonrecursive filters due to the added poles, but the stability may be severely threatened. In this paper an ANC system employing the adaptive recursive filter is proposed to enhance the speech corrupted by noise. And the stability of the adaptive recursive filter is guaranteed by employing the adaptive compensator.