The use of high-efficiency and energy-saving electricity gas coupling distribution network system provides an opportunity to consider increasing economic benefits and reducing environmental costs at the same time. In order to solve the problem of economic operation, a two-stage distributionally robust optimization model is proposed. The ambiguity uncertainty set of the probability distribution of wind power output prediction error is described by Wasserstein measure, and the distributionally robust optimization operation model of the combined electricity gas system of the electric hydrogen production plant considering the uncertainty of wind power output is constructed. The simulation results show that: Firstly, the introduction of electric hydrogen production device can effectively improve the electric gas coupling of distribution network system and improve the stability and economy of system operation. Secondly, considering the environmental cost, the pollutant emission of the electric gas coupling distribution network system of the electric hydrogen production unit is significantly reduced, ensuring the low-carbon operation of the system. Thirdly, distributionally robust optimization model can resist the interference of uncertain wind power and photovoltaic output, has relatively low conservatism and computational complexity, and has the characteristics of data-driven.