Abstract: A network synchronization model was proposed for two different complex networks with time-varying delay coupling. The two networks in the model were different in the number of nodes, topological structure, inner coupling, coupling delay, and node dynamics. Based on Lasalle's invariance principle, an adaptive controller was designed to achieve synchronization between these two networks. When the topological structures of two networks were fully unknown, the adaptive synchronization problem was also discussed. Numerical results were presented to verify the effectiveness of the proposed method.