Abstract: This paper focuses on the synchronization problems of general complex dynamical networks with time-varying delay. Two cases of the time-varying delay are considered---one being continuous-uniformly bounded and the other being differentiable-uniformly bounded with the derivative. And the coupling configuration matrix is also assumed to be asymmetric and reducible. Some new delay-dependent synchronization criteria are derived and a strategy for synchronization is presented based on a method of linear state feedback controller. The bounds of controller are solved by Matlab. Numerical examples are given to illustrate the effectiveness of the proposed synchronization criteria.