This note is concerned with the absolute stability for time-varying delay Lur’e system with sector-bounded nonlinearity. Improved delay-dependent and delay-derivative-dependent stability criteria are obtained in the form of linear matrix inequalities (LMIs) by constructing a modified augmented Lyapunov-Krasovskii (LK) functional without applying the model transformation or the bounding techniques for cross terms. Thus, the presented delay-dependent criteria are less conservative than those in the literature. Moreover, state feedback stabilizing controllers based on the proposed stability criteria are designed. Numerical example demonstrates the effectiveness and superiority of the proposed method.