Abstract: The stability of the interval time-varying delay systems is considered. By choosing the appropriate Lyapunov-Krasovskii functional, the sufficient conditions of delay-dependent stabilization are derived in terms of LMI (linear matrix inequality) based on integral equality approach (integral equality is constructed with free weighting matrices). There is no restriction on the derivative of the time-varying delay in the method, and it can be applied to the systems with quickly time-varying delays. Moreover, the integral equality approach possess much lower conservatism than the integral inequality approach. Finally, the simulation and numeric example prove that the method is effective and superior.