Quasi-synchronization of heterogenous dynamic networks is studied by using impulsive control in this paper. The asymmetric network connections are considered. First, the weighted average state is introduced as the virtual leader. By defining the synchronization error between the virtual leader and the network node, impulsive quasi-synchronization is analyzed and a criterion is derived to ensure quasi-synchronization in the delayed heterogenous network. Then delayed networks with symmetric connections and delay-free networks are studied, respectively, with simpler conditions obtained. Numerical simulations demonstrate the effectiveness of the derived results.