A new robust adaptive synchronization approach for the global synchronization of complex dynamical networks is proposed. Both the characteristics of the uncoupled nodes of the network and the coupling matrix are unknown, but only a time-varying coupling strength is used in this paper. Based on the LaSalle-Yoshizawa theorem and by introducing an update law, a sufficient condition of the global synchronization is obtained. The update law is only dependent on the states of the complex dynamical network, which do not need any other information such as the characteristic of the uncoupled nodes of the network and the second largest eigenvalue of the coupling matrix. Compared with the existing results, our synchronization strategy is still useful when the existing synchronization methods become invalid. Moreover, it is very convenient to use. An example of the complex network is finally used to verify the proposed theoretical result. (c) 2007 Elsevier B.V. All rights reserved.