Abstract: We design a non-fragile H_∞ filter for a class of discrete systems with infinite-distributed delays and randomly missing measurements. The proposal is made in consideration of the fact that current digital control systems are discrete ones. Random variables conformed to the Gaussian distribution are utilized in the gains of the filter to simulate the phenomenon of random gain variations in the discrete system. Infinite-distributed delays are then introduced to reflect the influence from the limited bandwidth in the networked control systems. Furthermore, the phenomenon of randomly missing measurements depicted by a Bernoulli distributed white sequence is considered. Based on Lyapunov stability theory, stochastic analysis technologyand LMI skills, the sufficient conditions for the existence of the non-fragile H_∞ filter are obtained. These conditions help make the filter error system asymptotically stable while simultaneously satisfying the performance index. As a result, the filter gains become solvable via the semi-definite programming technique. Finally, a numerical simulation is provided to illustrate the effectiveness of the research.