This paper considers the problem of delay-dependent exponential stability in mean square for stochastic systems with polytopic-type uncertainties and time-varying delay. Applying the descriptor model transformation and introducing free weighting matrices, a new type of Lyapunov-Krasovskii functional is constructed based on linear matrix inequalities (LMIs), and some new delay-dependent criteria are obtained. These criteria include the delay-independent/rate-dependent and delay-dependent/rate-independent exponential stability criteria. These new criteria are less conservative than existing ones. Numerical examples demonstrate that these new criteria are effective and are an improvement over existing ones. Applying the descriptor model transformation and introducing free weighting matrices, a new type of Lyapunov-Krasovskii functional is constructed based on on linear matrix inequalities (LMIs), and some new delay-dependent criteria are obtained. These criteria include the delay-independent / rate-dependent and delay-dependent / rate-independent exponential stability criteria. These new criteria are less conservative than the existing ones Numerical examples demonstrate that these new criteria are effective and are an improvement over existing ones.