Application of gas-fired units and power-to-gas devices promotes coupling between power system and natural gas system, and hence provides an alternative solution for the wind power integration. Also, the traditional stochastic optimization and robust optimization methods may result in uneconomic or conservative decisions in dealing with the uncertain problems. Thus, a data-driven based ... [Show full abstract] distributionally robust dispatch model for the integrated electricity and natural gas system is proposed in this paper, which is constructed in a two-stage optimization fashion. The day-ahead total cost for the integrated system is regarded as the optimization objective in the first stage where the forecast wind power information is also taken into consideration while the output adjustment of thermal generation units and the supply regulation of natural gas source are included in the real-time dispatch (second stage in this study). Besides, the norm-1 and norm-inf are simultaneously combined to constrain the confidence set of wind power probability distribution. Then the model is solved by the Column-and-Constraint Generation algorithm. Finally, numerical results verify the effectiveness of the proposed model.