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This paper discusses the synchronization problem for a class of Lurie type complex dynamical networks with time-varying delay. Based on a Lyapunov-Krasovskii functional, some new delay-dependent synchronization criteria are derived in the form of linear matrix inequalities by employing a delay decomposition and free matrix method. And a strategy for synchronization is presented based on a linear feedback controller. Some numerical examples are presented to illustrate the effectiveness and advantage of the proposed synchronization criteria. More less conservative is shown with comparison to the existing results.