Today, complex networks have attracted increasing attention from various fields of science and engineering. It has been demonstrated that many complex networks display various synchronization phenomena. In this note, we introduce a time-varying complex dynamical network model. We then further investigate its synchronization phenomenon and prove several network synchronization theorems. Especially, we show that synchronization of such a time-varying dynamical network is completely determined by the inner-coupling matrix, and by the eigenvalues and the corresponding eigenvectors of the coupling configuration matrix of the network.