Abstract: The optimal scheduling of electric-thermal combined energy system is of great significance to realize multi-energy complementarity,energy saving and emission reduction. The reinforcement learning method is used to realize the optimal scheduling of the energy system. The system state is used as a vector for learning and training,and the connection relationship between the system equipment is ignored. A reinforcement learning model of value distribution maximum entropy Actor-Critic algorithm based on graph neural network architecture is proposed. The electric-thermal combined energy system is modeled as graph structure data,which is input into the proposed reinforcement learning model,and the graph neural network model is used to extract the system state and output the scheduling strategy. The proposed model can make full use of the system topology information to achieve more effective exploration and learning. Simulation examples verify the effectiveness of the proposed method.