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In this paper,we investigate the locally and globally adaptive synchronization problem for an uncertain complex dynamical network with time-varying coupling delays based on the decentralized control.The coupling terms here are bounded by high-order polynomials with known gains that are ubiquitous in a large class of complex dynamical networks.We generalize the usual technology of searching for an appropriate coordinates transformation to change the network dynamics into a series of decoupled lower-dimensional systems.Several adaptive synchronization criteria are derived by constructing the Lyapunov-Krasovskii functional and Barbalat lemma,and the proposed criteria are simple in form and convenient for the practical engineering design.Numerical simulations illustrated by a nearest-neighbor coupling network verify the effectiveness of the proposed synchronization scheme.