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Because of the common phenomenon of coupled time-varying delay in the complex dynamical networks, the problem of impulsive synchronization in output coupled complex dynamical networks is investigated in this paper. In order to achieve synchronization of each node of a time-varying delayed complex network, we design an impulsive controller using output signals. Sufficient conditions are derived on the synchronization of the coupled time-varying delay complex dynamical networks under a given decay rate by using Lyapunov stability theorem and the comparison method. The chaotic Lorenz system is taken as the node dynamic for numerical simulation to illustrate the theoretical results and effectiveness of the proposed controller design procedure.