At present, island microgrid often adopts a hierarchical control structure to realize the stable, reliable and economic operation of systems, in which the first layer commonly uses a droop control. The droop control will lead to deviation of voltage and frequency from the given value, and reasonable distribution of reactive power cannot be realized, Therefore, many scholars have proposed to introduce the multi-agent consistency algorithm into the secondary control of island microgrid. Through sparse communication with adjacent distributed generators, the problems of complex communication network structure and difficult calculation caused by centralized control can be effectively solved. This paper introduces the hierarchical control structure of island microgrid and expounds in detail application of multi-agent consistency algorithm in the secondary control of island microgrid. Combined with practical problems in the operation of island microgrid, improvement of multi-agent consistency algorithm is introduced for the secondary control of island microgrid regarding convergence speed, anti-interference control, communication delay and event triggering control, with also development direction of multi-agent technology in secondary control of island microgrid being summarized．