This paper investigates the problems of H∞ disturbance attenuation and H∞ filtering for Markovian jump systems with interval time-varying delays. In terms of linear matrix inequalities, a less conservative delay-range-dependent H∞ performance condition for Markovian jump systems is proposed by constructing a different Lyapunov–Krasovskii functional. The resulting criterion has advantages over some previous ones in that they involve fewer matrix variables, but has less conservatism. Based on this new condition, an improved H∞ filtering algorithm is developed. Numerical examples are provided to demonstrate the efficiency and reduced conservatism of the results in this paper. Copyright © 2009 John Wiley & Sons, Ltd.