Investigates the problem of stability of neutral systems with time-varying delay by employing an augmented Lyapunov-Krasovskii functional and a free-weighting matrix approach. Takes into account the relationship among the time-varying delay, its upper bound and their differences, retains useful terms in the derivative of Lyapunov-Krasovskii functional, and obtains less conservative LMI-based delay-dependent stability conditions. A numerical example shows that the results obtained in this study are better than published results.