In microgrid (MG) systems, traditional centralised energy trading models can lead to issues such as low energy efficiency due to unstable energy supply and lack of flexibility. Peer‐to‐peer (P2P) trading models have been widely used due to their advantages in promoting the sustainable development of renewable energy and reducing energy trading costs. However, P2P multi‐energy trading requires mutual agreements between two microgrids (MGs), and the uncertainties of renewable energy and load affects energy supply security. To address these issues, this article proposed a distributed robust operation strategy based on P2P multi‐energy trading for multi‐microgrid (MMG) systems. Firstly, a two‐stage robust optimisation (TRO) method was adopted to consider the uncertainties of P2P multi‐energy trading between MGs, which reduced the conservatism of robust optimisation (RO). Secondly, a TRO model for P2P multi‐energy trading among MGs was established based on the Nash bargaining theory, where each MG negotiates with others based on their energy contributions in the cooperation. Additionally, a distributed algorithm was used to protect the privacy of each MG. Finally, the simulation results based on three MGs showed that the proposed approach can achieve a fair distribution of cooperative interests and effectively promote cooperation among MGs.