Modern trends in improving environmental safety have determined the urgency in creating innovative technologies that allow the production of electricity and hydrogen without the emission of harmful substances. However, at the moment, there are not so many technical solutions offering the combined production of these useful products with a high degree of efficiency and environmental friendliness. The transition to oxy-fuel combustion power cycles for the co-production of electricity and hydrogen is a prospective way to decrease carbon dioxide emissions into the atmosphere from the energy sector. To achieve zero emissions, the semi-closed oxy-fuel combustion cycle is combined with a steam methane reformer, which has a high energy efficiency through reducing losses in the steam turbine condenser. The modeling methodology has been described in detail, including the approaches to defining the working fluid properties and mathematical models of the different steam methane reforming plants and the oxy-fuel combustion power plant. According to the results of the thermodynamic analysis of the steam methane reforming plant, it was found that an increase in the temperature from 850 to 1000 °C leads to a decrease in the mass flow fuel by 16.3% due to the shift towards a direct reaction. Moreover, the optimal temperature in the reformer lies in the range of 900–950 °C. A comparison of the energetic and ecological characteristics of various steam methane reformer units showed that the scheme with oxy-fuel combustion is better compared to the scheme with CO2 capture by absorption in monoethanolamine; the efficiency is 6.9% higher and emissions of carbon dioxide are 22 times lower. According to the results of the thermodynamic analysis of a novel oxy-fuel combustion power cycle, it was found that its performance varied regarding the range of electricity production (123.6–370 MW) and hydrogen production (0–10.8 kg/s). The efficiency of the oxy-fuel combustion power cycle varies in the range of 47.2–70.1%. Based on the results of the operation regimes analysis, the energy complex performance map has been developed, allowing identification of the efficiency and working fluid massflow by net power and produced hydrogen massflow.