This paper investigated the adaptive synchronization of a driveresponse dynamical network, in which each node is a chaotic system with unkonwn parameters. Based on the Lyapunov stability theory and LaSalle’s invariant set theory, suitable controllers and parameters update laws were designed to achieve synchronization between the drive system and response dynamical network. A weighted network and a scalefree network were used as examples to verify theoretical results. In addition, with the same network topology, synchronization time of different dynamics was compared. Numerical simulations show the effectiveness of the control scheme.