We scrutinize the problem of robust H∞control for a class of Markovian jump uncertain systems with interval time-varying and distributed delays. The Markovian jumping parameters are modeled as a continuous-time finite-state Markov chain. The main aim is to design a delay-dependent robust H∞control synthesis which ensures the mean-square asymptotic stability of the equilibrium point. By constructing a suitable Lyapunov–Krasovskii functional (LKF), sufficient conditions for delay-dependent robust H∞control criteria are obtained in terms of linear matrix inequalities (LMIs). The advantage of the proposed method is illustrated by numerical examples. The results are also compared with the existing results to show the less conservativeness.