Fault recovery in an integrated electricity and natural-gas Active Distribution Network (ADN) is very important for improving the reliability of the system. To solve the problem of fault recovery in an integrated electricity and natural-gas ADN, a robust optimization theory is used considering system uncertainty. In the model, the wind photovoltaic output and the fault recovery scheme are considered as natural decision-makers and system decision-makers respectively to make them game. The natural decision-maker model is established with maximizing the power loss load as the objective function, taking into account the uncertainty constraints of the interval form; the system decision-maker model is established with minimizing the power loss load, taking into account the constraints of electricity and natural-gas integration, and radiation, power balance and operation constraints of the electrical energy network. Based on a two-stage relaxation method, the solution steps for the robust optimization model are designed. Finally, an example is given to verify the validity of the model. This work is supported by the National Natural Science Foundation of China (No. 61873225) and the Beijing- Tianjin-Hebei Cooperation Special Program of Natural Science Foundation of Hebei Province (No. F2016203507).