Integrated energy system (IES) is an advanced configuration that combines electrical energy, thermal energy, and renewable energy, into a unified system. In recent years, the architecture of IES has gradually changed from vertical integration to interactive competition, and its distributed characteristics have become increasingly evident. Therefore, traditional centralized optimization strategies can no longer meet the current practical situation. In this paper, a low- carbon optimization dispatch for IES based on Stackelberg game and kriging metamodel is proposed. In order to address this problem, firstly, three typical models containing hydrogen blending gas technology and a kind of ladder- type carbon trading mechanism considering reward and punishment (RP-LCTM) are established. Secondly an integrated energy manager (IEM) is introduced and a Stackelberg game model with the IEM as the leader and three typical IESs as followers is established. Finally, the kriging metamodel is used to optimize the transaction electricity price. During the game process, the IPSO algorithm is used to optimize electricity prices in key price regions. At last, an experimental example is utilized to demonstrate the effectiveness of the proposed method.