The actual travel behavior of electric vehicles has a certain degree of randomness and uncertainty, the spatial and temporal distribution characteristics of their charging loads pose double challenges to the low-carbon economic operation of the integrated energy system in parks. To solve the imbalance between the supply and demand of renewable energy existing in the park and the overall economic problems of integrated energy systems in parks, a low-carbon operation model of integrated energy systems in parks that considers the travel chain of electric vehicles is presented. Firstly, the composition and operation mechanism of integrated energy systems in parks containing EVs is introduced, and the microgrid operator model containing the green certificate-carbon trading mechanism and the electrical and thermal loads of user aggregator are established, respectively. Secondly, the nonhomogeneous semi-Markov chain theory is used to simulate the travel behavior of EVs, construct a stochastic travel chain for EVs, and establish a charging decision mechanism by combining the transfer law and residence time distribution of vehicles between states. Finally, to maximize the interests of each subject and reduce the carbon emissions in the park, a Stackelberg game model between users containing electric vehicles and the microgrid operator is constructed. The results show that the established model can meet the charging demand of EVs under the complex travel chain, effectively increase the economic and environmental benefits of integrated energy systems in parks.