In the integrated energy system with a high proportion of new energy including power to hydrogen (P2H), the uncertainty of new energy has a great impact on the system, and the flexibility and adequacy of the system have become important factors. A supply and demand model of various types of flexible resources in an integrated energy system with P2H is established, and the flexible adjustment capability of the system is described. The base uncertainty ensemble method in robust optimization is used to describe the wind power forecast error. The forecast error and economic dispatch decision makers are regarded as the competition of the game. Based on zero-sum game theory, a new robust optimization model of an integrated energy system with P2H considering flexibility balance is established. On the basis of robust optimization, the influence of new energy uncertainty and flexible supply and demand balance in the system is analyzed. A simulation analysis of an actual integrated energy system with P2H in Northeast China shows that the proposed method can effectively deal with the uncertainty of wind power output, and take into account the economic operation and flexibility of the system.