This study presents design and robust stability analysis of a novel version of RLS-type adaptive IIR filter in the modified filtered-x structure. The derivation of the algorithm is by transforming the original ANVC problem to an output-error identification problem without assuming that the slow adaptation condition holds. By considering fast adaptation of the filter weights and also the assumption that nonparametric uncertainty exists in the estimation of the secondary path, the stability of the proposed algorithm is analyzed using Lyapanov theory. In fact by introducing a time-varying scalar parameter in the adaptation, a sufficient condition based on the value of this parameter and the size of the uncertainty is derived