The distributed control of a multi-microgrid (MMG) system composed of neighboring microgrids (MGs) is much more complex than that of an MG. In this paper, a fully distributed control method with fault tolerance control for MMG systems is proposed, which is a two-layer model, where a communication network composed of agents is the top layer, while an MMG is the bottom layer. Further, a systematic method is presented to obtain a set of distributed control laws for agents from any given communication network. The communication network consists of two types of subgraphs, a within-MG subgraph and a between-MG subgraph. Moreover, the control laws derived from the within-MG subgraph ensure the supply-demand balance and the proportional outputs of distributed generators (DGs) in each MG, while the control laws derived from the between-MG subgraph coordinate MGs to achieve the power balance of the MMG system. Furthermore, two theorems and a proposition are proved, which state the convergence of the derived control laws. Finally, simulations are carried out on the MMG model in MATLAB/Simulink. The results show that the frequencies and voltages in MGs stay at the prescribed values, and the proportional outputs are achieved, when both loads and environmental conditions fluctuate. Furthermore, our distributed method has higher tolerance to the failures of agents, when compared to a centralized method. (C) 2018 Elsevier Ltd. All rights reserved.