This paper deals with the robust stability of polytopic-type uncertain nonlinear stochastic systems with distributed and discrete delays.In the investigation,the sufficient conditions for the delay-dependent and parameter-dependent robust stability of the systems are determined on the basis of the parameter-dependent Lyapunov-Krasovskii functional and by using the stochastic Lyapunov stability theory and the free-weighting matrix method.Then the stability criteria of the systems are proposed in the form of linear matrix inequality.A numerical example is finally presented to demonstrate the effectiveness of the proposed method.