With the increasing coupling between power system and natural gas system, the integrated energy system with power grid as the core emerges as the times require. However, under uncertain conditions, the current planning methods still can not guarantee the best interests of each manufacturer. Therefore, this paper proposes a collaborative planning method for electric-gas system based on non-cooperative game theory. Firstly, the integrated non-linear programming model of wind turbine, gas turbine, electric converter, transmission line and natural gas pipeline in the power-gas integrated system is established with each energy unit and electric and gas network company as independent interest groups and the maximum annual net income as the optimization objective. Aiming at the uncertainties of wind power and load , the conservativeness of classical two-stage robust optimization, an improved two-stage robust optimization method is proposed. It is expected in scenario optimization and feasible in any scenario. Finally, the modified IEEE39-bus power system and Belgium 20-bus natural gas system are used to construct the electrical-gas network, which verifies the effectiveness of the model and the algorithm.