The nonfragile H∞ filtering problem affected by finite word length (FWL) for linear discrete-time systems is investigated in this paper. The filter to be designed is assumed to be with additive gain variations, which reflect the FWL effects on filter implementation. A notion of structured vertex separator is proposed to deal with the problem and exploited to develop sufficient conditions for the nonfragile H∞ filter design in terms of a set of linear matrix inequalities (LMIs). The design renders the augmented system asymptotically stable and guarantees the H∞ attenuation level less than a prescribed level. A numerical example is given to illustrate the effect of the proposed method.