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The paper aims to present a new scheme of synchronization-based topology identification for a class of weighted general complex dynamical networks with time-varying coupling delays. By combining the adaptive control method and the Razumikhin-type theorem, a new feedback technique to identify the exact topology of the dynamical networks with time-varying coupling delay has been proposed. In comparison with the previous methods, the time-varying coupling delay must not slowly vary with time, that is, the derivative of time-varying delay can be larger than 1. The simulation results show the effectiveness of the proposed scheme.