In this paper, an adaptive Infinite Impulse Response (IIR) filter algorithm using output error method, which prevents poles of a system transfer function from being out of unit circle, is proposed, and it is proved that the proposed algorithm always satisfies hyperstability. The proposed algorithm is applied to an Adaptive Noise Canceller (ANC), and compared with a Least Square (LS) method adaptive IIR filter algorithm and an adaptive Finite Inpulse Response (FIR) filter algorithm. As a result, the validity of the proposed algorithm is proved.