This paper develops new stability criteria for T-S fuzzy systems with interval time-varying delay and parameter uncertainties. The derived criteria are delay- dependent, and are less conservative and more computationally efficient than those obtained from existing methods. The basic ideas are to use appropriate Lyapunov-Krasovskii function and augmented Lyapunov-Krasovskii functional, to construct uncorrelated augmented matrix (UAM), and to deal with cross terms in the UAM through improved Jessen inequality. Using this approach, neither free weighing matrices nor model transformations are necessary in our derivation. The paper also shows that some existing results are special cases of the results derived in this paper. Numerical examples are given to demonstrate the effectiveness of the developed stability criteria.