With the rapid development of wind power generation, the difficulty of renewable energy consumption has become an urgent problem in the power and energy fields. The integrated electricity and natural-gas energy systems (IENES) is an inevitable choice to promote the renewable energy consumption, improve the energy comprehensive utilization and promote the energy sustainable development. The state mutation, failure or even off-network of wind turbines will cause electrical equipment safety, power system cascading failure and stability problems. Gas turbines and power-to-gas (P2G) devices have fast and flexible power control capabilities, especially the adequate energy reserves of gas systems provide a large margin for fault control of power systems. The close interaction between the power system and the gas system provides an effective technical solution to solve the grid failure safety problem caused by the new energy source. At present, there are few studies on the scheduling of IENES, and almost no research take the risks of IENES into account. However, the fault risk of power system in IENES is different from that in the single power system. The influence of P2G and gas turbines on the risk of the power system cannot be ignored, so that the traditional scheduling method in power system is difficult to apply in IENES. Therefore, the risk reduction scheduling for IENES considering P2G was proposed to resolve the contradiction between risk and power generation cost. Firstly, the operating characteristics of the IENES and the fault mechanisms of the wind turbine were analyzed. Secondly, the operational risk index of the IENES under the wind turbines failure was established. Then, the multi-objective optimization scheduling model based on this risk index was established, and the objective are minimizing the operating risk and minimizing the coal consumption of the thermal power units. Finally, the model proposed in this paper was proved to reduce the system risk and improve wind power consumption effectively according to the examples.