With the depletion of sources of primary energy across the world, the prospect of a global energy crisis in the near future has raised considerable concern. Among the many sources of clean energy, wind energy is considered to be the most effective means of sustainable and environmentally friendly energy. Traditional systems of energy based on oil and natural gas still operate in a discrete manner, and the promise offered by the mutual coordination between energy systems to draw complementary benefits has not yet been fully exploited. This has prompted all energy sectors to examine the optimal integration of interconnected gas–electricity energy systems. In this context, this study proposes a multi‐objective collaborative operational optimization model of P2G for an interconnected, integrated gas–electricity energy system in case of uncertain wind power. Based on the effect of carbon capture by using P2G, the effect of coupling gas and electricity, and the cost of low‐capacity reserves, the authors use conditional risk values to design four targets of optimization—the operating cost of the system, rate of consumption of the natural gas system, total carbon emissions and capacity stand‐by cost—according to the power system, natural gas system, thermal energy system, and their elements of coupling from multiple perspectives to clarify the constraints on the model. Moreover, to reduce the likelihood of the optimal solution falling into the local optimum, the improved cuckoo algorithm is used to optimize the multi‐objective scheduling model. The authors used a 10‐node power system and a six‐node natural gas system as examples for simulation to verify the proposed model. The results of empirical analysis show the following: (a) Once the P2G equipment had been connected, it reduced the total operating cost and improved the consumption of wind power of the natural gas system regardless of whether backup services were provided. (b) The P2G equipment could be combined with gas‐fired CHP units to “cut peaks and fill valleys” in the electrical load of the power system. These results verify the effectiveness of the proposed multi‐objective optimal dispatch model of an interconnected gas–electricity energy system.