This paper, considered the synchronization problem in a complex delayed dynamical network with impulsive coupling.A sufficient condition for ensuring network synchronization was derived analytically based on extended Halanay inequality on delayed dynamical systems with impulse.It is shown that such a complex dynamical network can always achieve synchronization even when there exist instantaneous connections among the nodes at a series of instants.Furthermore,the results were applied to a typical scale-free (SF) complex networks consisting of coupled chaotic FHN neuron oscillators,and numerical simulations were carried out to verify and also visualize the theoretical results.