In this paper, a distributed control strategy based on consensus algorithm is proposed to deal with the secondary frequency control problem for islanded AC microgrid. The proposed strategy allows the active power setpoints of each distributed generator (DG) unit to be updated in the presence of time-varying bounded communication delays in the distributed communication network, thereby restoring the average frequency of the system to a reference value. In order to further reduce the communication burden, an event-driven control method is adopted, that is, the proposed strategy is started only when the system frequency deviation is excessive. Compared with the traditional control method, the proposed strategy only needs the information of the DG itself and its neighbors to achieve the control target, eliminating the need for the microgrid central controller (MGCC) and improving the reliability and flexibility of the system. Simulation results validate the effectiveness of our proposed control strategy.