The current theoretical study on the synchronization mechanism of complex networks mainly focuses on fixed connected topology or switching balanced topology, which is heavily based on constructing common smooth Lyapunov functions. However, for complex networks with nonlinear node dynamics, it is still unknown whether such kind of networks can synchronize under the condition of switching, directed, and disconnected topology. By employing the ideas of sequential connectivity and joint connectivity, this paper finds that complex networks with one-sided Lipschitz node dynamics can realize synchronization even if the network topology is not connected at any time instant. By iteratively estimating the maximal distance between different nodes, this paper gives several sufficient conditions on synchronization of nonlinear complex networks under switching disconnected topology. Finally, simulation examples validate the main results. (C) 2016 Elsevier Ltd. All rights reserved.