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This paper revisits the problem of synchronization stability for general complex dynamical networks with coupling delays. A new delay-dependent criterion is derived by introducing a new kind of Lyapunov-Krasovskii functional and is formulated in terms of a linear matrix inequality, which can be readily solved via standard software. This new criterion based on a delay fractioning approach is proved to be much less conservative and the conservatism could be notably reduced by thinning the delay fractioning. Furthermore, the resulting criterion is further extended to the synchronization stability analysis of complex dynamical networks with time-varying structured uncertainties. Two numerical examples are provided to show the effectiveness and advantage of the proposed results. [ABSTRACT FROM AUTHOR]