Abstract: In this paper, we investigate the robust stochastic stability for a class of continuous time-varying delay uncertain systems with Markovian switching. The Markovian switching considered here forms a continuous-time discrete-time homogeneous Markov process. In terms of stochastic Lyapunov function method and linear matrix inequality, sufficient criterion for testing the robust stochastic stability of systems are proposed respectively. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.