Abstract: The problem of global synchronization was studied for a class of complex dynamical networks composed of Lur'e systems. With the feedback strategy applied to a small part of the nodes in a large-size network, all the nodes in the whole weighted time-delay network become synchronous. Based on the absolute stability theory, the delay-independent and delay-dependent asymptotical stability criteria are derived separately to ensure the global synchronization of a network. In some particular cases, the synchronization of whole network is available only if pinning the control on a single node in the network. Numerical simulation results verified the effectiveness of the conclusion as above.