In this paper, the problem of the stability for a class of stochastic systems with time-varying interval delay is investigated. Through constructing a novel Lyapunov-Krasovskii functional and utilizing the information of both the lower and upper bounds of the delay, the delay-dependent sufficient criteria are derived in terms of linear matrix inequalities (LMIs). Neither model transformations nor bounding techniques for cross terms is employed, so the derived criteria are less conservative than the existing results. Meanwhile, the computational complexity of the obtained stability conditions is reduced because fewer variables are involved. Numerical examples are given to show the effectiveness and the benefits of the proposed method.