In this paper, an agent-based decentralized control model for islanded microgrids is proposed, which consists of a two-layer control structure. The bottom layer is the electrical distribution microgrid, while the top layer is the communication network composed of agents. An agent is regarded as a local control processor together with communication devices, so agents can collect present states of distributed generators and loads, when communication lines are added between two layers. Moreover, each agent can also exchange information with its neighboring agents of the network. After information is processed according to control laws, agents adjust the production of distributed generators to which they connect. The main contributions of this paper are (i) an agent-based model for decentralized secondary control is introduced and the rules to establish the communication network are given; (ii) a systematic method is presented, which can be used to derive a set of control laws for agents from any given communication network, where only local information is needed. Furthermore, it has been seen that the output power supplied by distributed generators satisfies the load demand in the microgrid, when agents use the proposed control laws. Finally, the simulation results show that frequency and voltage fluctuations are small and meet the requirements.