Summary: By using Lyapunov-Krasovskii functional approach, we derive novel synchronization criteria in the form of linear matrix inequalities for singular complex dynamical networks with delayed coupling and non-delayed coupling. The convexity of matrix functions and the free-weighting matrix method are fully exploited to reduce the conservatism of the results we obtained. Numerical examples are presented to illustrate the efficiency and less conservatism of the proposed method.