Complex networks have attracted much attention from various fields of sciences and engineering over the last ten years. To reveal the dynamical mechanism of synchronization in complex networks with time delays, a general complex dynamical network with delayed nodes is introduced. Based on this model, we further investigate the adaptive feedback synchronization and obtain several novel criteria for globally exponentially asymptotic synchronization. In particular, our hypotheses and the proposed adaptive controllers for network synchronization are very simple and can be readily applied in practical applications. Finally, numerical simulations are provided to illustrate the effectiveness of the proposed synchronization criteria.