Gas-fired power units (GFUs) are the best technology in recent years due to lower natural gas prices, higher energy transformation performance, and lower CO2 emission, as compared to the conventional power units (CPUs). A permanent storage facility called power-to-gas (P2G) technology can provide adaptation of ever-increasing renewable energy sources (RESs) fluctuations in power system operations, as well as reduce dependency to buy natural gas from the gas network. High investment and utilization expenditures of state-of-the-art P2G technology do not lead to economically effective operation individually. Therefore, in the present paper, an integrated GFUs-P2G-wind power unit (WPU) system is proposed to determine its optimal bidding strategy in the day-ahead energy market. A robust optimization approach is also taken into account to accommodate the proposed bidding strategy within the electricity price uncertainty environment. This problem was studied by using a case study that included a P2G facility, GFU, and WPUs to investigate the effectiveness and capability of the proposed robust bidding strategy in the day-ahead energy market. Simulation results indicate that the obtained profit increase by introducing the integrated energy system, and the P2G facility has a significant effect on participating GFUs, which have gas-consumption limitations in order to achieve maximum profit. Moreover, as it can be said, the amount of purchased natural gas is decreased in the situations, which do not have any gas-consumption limitations. Furthermore, the proposed system’s operation in the robust environment provides more robustness against electricity price deviations, although it leads to lower profit. In addition, deploying P2G technology causes about 1% incrementation in the introduced system profit.