The networked Multi-Energy Microgrids (MEMGs) can significantly improve the economic efficiency of operation through energy cooperation and complementarity. However, the complex energy trading mechanism and multi-energy coupling decision process present various challenges for the optimal operation of MEMGs, such as the large decision space and the difficulty of converging to the global optimal solution. This study presents a novel energy management method for MEMG based on an improved Deep Q-network (IDQN) to solve these problems. Firstly, the equivalent model of an external interactive environment is constructed for each MEMG by using a novel Kriging surrogate enhanced Gate Recurrent Unit-Temporal Convolutional Network (GRU-TCN), which requires only the accessible energy exchange data and the public and independent information as input. The computational complexity of the reinforcement learning reward function is reduced accordingly by using this equivalent model. Subsequently, an improved k-crossover sampling strategy with reduced access frequency of the low reward actions is proposed to replace the traditional.-greedy strategy to further improve the original DQN. This effectively addresses the problem of inefficient exploration in a large-scale action space. Lastly, the proposed method is verified using a test system with three MEMGs. The result demonstrates that the proposed IDQN method presents better convergence and stability than the traditional DQN, and presents better energy management and operational efficiency.