This note is concerned with the absolute stability analysis for time-delay Lurie control systems with nonlinearity located in an infinite sector and finite one. By using a new Lyapunov-Krasovskii functional that splits the whole delay interval into two subintervals and defines a different energy function on each subinterval and introducing some free-weighting matrices, some new delay-dependent robustly absolute stability criteria are presented in terms of strict linear matrix inequalities (LMIs). The obtained delay-dependent criteria are less conservative than previous ones, as arc illustrated by numerical examples.