AbstractThe IIR type adaptive algorithm can be classified by its structure into the series‐parallel type and parallel type. Most of the FIR type adaptive algorithms can be applied to the series‐parallel type. However, this type has the problem that a bias error is produced in the estimated transfer function in the presence of observation noise. On the other hand, while the parallel type is expected to suffer less from observation noise, it may produce oscillation. It is difficult to insure the convergence and only the method by Landau is known. His method, however, necessitates matrix manipulation, which increases the computational complexity. Discussion has not been made on convergence when observation noise is present. This paper shows that the high‐speed least‐mean‐square method can be applied to the parallel type. In this method the computational complexity is small, being proportional to the number of coefficients. The convergences of the proposed method and the least‐mean‐square method applied to the series‐parallel type are analytically compared in the presence of observation noise.