Abstract: With the construction of new power systems with high proportion of renewable energy and high power electronics, the grid-forming converters have the advantage of flexibility and controllability, which can provide voltage and frequency support for the new power system with low rotational inertia and weak damping. In this paper, considering the communication delays, a distributed fractional-order predefined-time sliding mode controller is proposed to improve the stability of the islanded AC microgrid(MG) system based on grid-forming converters. First, considering the time delay of the distributed communication network, the model of islanded AC MG with communication delay is established. Then, based on Artstein transformations, the islanded AC MG system with communication delay is transformed into a model without delay. In addition, based on fractional-order calculus, distributed control, sliding-mode control theory and predefined-time stability theorem, a distributed predefined-time fractional-order sliding-mode control method considering communication delay is proposed to improve the stability of the islanded AC MG system. Finally, the effectiveness of the proposed control method is verified by simulation and the islanded AC MG system can restore the stable operation with a large delay margin.