Bidirectional coupling systems for electricity and natural gas composed of gas units and power-to-gas (P2G) facilities improve the interactions between different energy systems. In this paper, a combined optimization planning method for an electricity-natural gas coupling system with P2G was studied. Firstly, the characteristics of the component model of the electricity-natural gas coupling system were analyzed. The optimization planning model for the electricity-natural gas coupling system was established with the goal of minimizing the sum of the annual investment costs and the annual operation costs. Based on the established model, the construction statuses for different types of units, power lines, and pipelines and the output distribution values for gas units and P2G stations were optimized. Then, the immune algorithm was proposed to solve the optimization planning model. Finally, an electricity-natural gas coupling system composed of a seven-node natural gas system and a nine-node power system was taken as an example to verify the rationality and effectiveness of the model under different scenarios.