Abstract This paper investigates the problem of L2-L∞ filtering for neutral Markovian switching systems with partially unknown transition probabilities for different system mode and delay mode. The system under consideration involves discrete and mode-dependent time-varying delays. Based on the Lyapunov–Krasovskii functional, an approach to design a filter such that the filtering error system is stochastically stable with a prescribed L2-L∞ performance. By using free weighting matrices, free-connection weighting matrix method and convex combination approach, sufficient conditions for the existence of L2-L∞ filters are expressed in terms of linear matrix inequalities (LMIs), which can be solved by using Matlab LMI control toolbox. A numerical example is given to illustrate the effectiveness and potential of the proposed method.