Abstract: In view of the stability analysis of linear discrete systems, an intense research has been conducted by adopting an improved discrete Wirtinger-based inequality. A new stability criterion of linear discrete systems with interval time-varying delay is derived, which yields less conservative stability conditions. By definition of a novel auxiliary function, we propose a better integral inequality and receive a tighter stability condition as compared to the recently results such as discrete Jensen inequality, discrete Wirtinger-based inequality. Based on the new inequality, we construct a dedicated Lyapunov-Krasovskii functional and obtain a tighter estimation of the derivative of Lyapunov-Krasovskii functional in terms of the new inequality. Finally, two numerical examples are given to demonstrate the efficiency of our new methods.