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This paper presents a study on the problem of designing non-fragile H∞ filters with sparse structure for linear discrete-time systems. The filters to be designed with sparse structure are assumed to be with additive gain variations, which are resulted from filters implementations. Firstly, a class of sparse structures based on the observable standard form is specified from a given fully parameterized H∞ filter. Then, an LMI-based procedure for designing non-fragile H∞ filters with the sparse structure is provided. The resulting design guarantees the augmented system asymptotically stable and the H∞ attenuation level less than a prescribed level. A numerical example is given to illustrate the proposed method.