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In this paper, finite-time synchronization for a class of Markovian jump complex networks (MJCNs) with generally uncertain transition rates (GUTRs) is considered. In this GUTR network model, each transition rate can be completely unknown or only its estimate value is known. This new uncertain model is more general than partly unknown transition rates (PUTRs). By constructing a suitable stochastic Lyapunov-Krasovskii function, using finitetime stability theorem and pinning control approaches, a sufficient finite-time synchronization criterion is derived in term of linear matrix inequalities (LMIs), which is easy to solve with the help of the LMI toolbox in Matlab. Finally, theoretical results are supported by numerical simulations.