Abstract: The distributed control methods of microgrids relie on sparse communication networks, which may seriously affect the control effect under cyber-attacks, and even cause the system instability. Considering the false data injection（FDI） attack, first, a mathematical model of FDI attack is established for isolated AC microgrids in distributed control mode. Secondly, the vulnerability of the system under FDI attack is analyzed. On this basis, a distributed resilient control method of microgrid against FDI attacks based on the adaptive control theory is proposed. The proposed method can achieve the established control objectives under bounded or unbounded FDI attacks and has good dynamic performance. Then, the convergence of distributed resilient controller is proven strictly by Lyapunov theory. Finally, the effectiveness of the proposed control method is verified by time-domain simulation in a variety of scenarios.