With the gradual marketization of energy trading, the retail price pricing strategy of microgrid service provider in a multi-microgrid system including electric-gas-heat will affect the operation of the system and the interests of all participants. In order to study the pricing strategy of microgrid service providers, this paper firstly describes the internal transaction process of the electric-gas-heat multi-microgrid system and establishes the system model. This pricing problem is then described as a Stackelberg game, and it shows that there is a unique equilibrium point for this game. In order to protect the privacy of each subject, this paper proposes a solution method based on reinforcement learning to solve the Stackelberg game with time coupling. The case study shows that this method can accurately and effectively solve the proposed pricing strategy problem, and the microgrid service providers and all the microgrids have adopted effective strategies to ensure their own interests. At the same time, the method effectively protects the privacy of market participants and exhibits good computing performance.