In this paper, the finite-time synchronization problem of complex dynamic networks with time delay is studied via aperiodically intermittent control. By compared with the existed results concerning aperiodically intermittent control, some new results are obtained to guarantee the synchronization of networks in a finite time. Especially, a new lemma is proposed to reduce the convergence time. In addition, based on aperiodically intermittent control scheme, the essential condition ensuring finite-time synchronization of dynamic networks is also obtained, and the convergence time is closely related to the topological structure of networks and the maximum ratio of the rest width to the aperiodic time span. Finally, a numerical example is provided to verify the validness of the proposed theoretical results.