This paper investigates the problem of absolute stability of Lurie nonlinear systems with time-varying delay by employing an augmented Lyapunov-Krasovskii functional and a free-weighting matrix approach. Some useful terms have been retained, which were used to be ignored in the derivative of Lyapunov-Krasovskii functional. Furthermore, the relationship among the time-varying delay, its upper bound and their difference is taken adequately into account. As a result, some less conservative delay-dependent stability conditions are obtained in terms of linear matrix inequalities (LMIs). A numerical example is given to show that the results obtained in this paper are better than the existing ones.