This study proposes a cooperative secondary voltage control scheme in islanded microgrids, which can be seen as multi-agent systems with distributed generators being agents. Therefore, the voltage deviation caused by the primary control level can be compensated autonomously in a microgrid using a directed communication graph. An auxiliary centralised event-triggered controller is designed to deal with feedback control law. In this scheme, the estimates of agents are used to replace their actual values for feedback control. All agents receive the same event-triggered time from the auxiliary centralised controller. Thus, communication between agents is only needed when events are triggered, which highly reduces the burden of the communication network to make the control structure be more reliable. The stability analysis is also presented here. Simulation results based on an islanded microgrid test system in PSCAD/EMTDC are provided to validate the effectiveness of the proposed control strategy.