Time-triggered impulsive control of complex homogeneous dynamical networks has received wide attention due to its occasional occupation of the communication channels. This report is devoted to quasi-synchronization of heterogeneous dynamical networks via event-triggered impulsive control. Two kinds of triggered mechanisms, i.e., the centralized event-triggered mechanism in which the control is updated based upon all the state information, and the distributed event-triggered mechanism where the control is updated based on the state information of each node and its neighboring nodes, are proposed respectively such that synchronization error between heterogeneous dynamical networks and a virtual leader is not more than a nonzero bound. What is more, the Zeno-behavior is shown to be excluded. It is found that distributed event-triggered impulsive control has the advantages of low energy consumption and far less taking up the communication channels over the time-triggered impulsive control. Two numerical examples are conducted to illustrate the effectiveness of the proposed event-triggered impulsive control.