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This paper proposes a novel H∞ filtering technique for a class of discrete-time fuzzy systems. First, a novel kind of fuzzy H∞ filter, which is homogenous polynomially parameter dependent on membership functions with an arbitrary degree, is developed to guarantee the asymptotic stability and a prescribed H∞ performance of the filtering error system. Second, relaxed conditions for H∞ performance analysis are proposed by using a new fuzzy Lyapunov function and the Finsler lemma with homogenous polynomial matrix Lagrange multipliers. Then, based on a new kind of slack variable technique, relaxed linear matrix inequality-based H∞ filtering conditions are proposed. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed approach.