The fast H∞ filter is developed by one of the authors, and its practical use in industries is expected. This paper derives a linear propagation model of numerical errors in the recursive variables of the fast H∞ filter, and then theoretically analyzes the stability of the filter. Based on the analyzed results, a numerical stabilization method of the fast H∞ filter is proposed with the error feedback control in the backward prediction. Also, the effectiveness of the stabilization method is verified using numerical examples.