To reduce greenhouse gas emissions from natural gas use, utilities are investigating the potential of adding hydrogen to their distribution grids. This will reduce the carbon dioxide emissions from grid-connected engines used for stationary power generation, and it may also impact their power output and efficiency. Promisingly, hydrogen and natural gas mixtures have shown encouraging results regarding engine power output, pollutant emissions, and thermal efficiency in well-controlled on-road vehicle applications. This work investigates the effects of adding hydrogen to the natural gas fuel for a lean-burn spark-ignited four-stroke, 8.9 liter eight-cylinder naturally aspirated engine used in a commercial stationary power generation application via an engine model developed in the GT-SUITETM modelling environment. The model was validated for fuel consumption, air flow, and exhaust temperature at two operating modes. The focus of the work was to assess the sensitivity of the engine’s power output, brake thermal efficiency, and pollutant emissions to blends of methane with 0–30% (by volume) hydrogen. Without adjusting for the change in fuel energy, the engine power output dropped by approximately 23% when methane was mixed with 30% by volume hydrogen. It was found that increasing the fueling rate to maintain a constant equivalence ratio prevented this drop in power and reduced carbon dioxide emissions by almost 4.5%. In addition, optimizing the spark timing could partially offset the increases in in-cylinder burned and unburned gas temperatures and in-cylinder pressures that resulted from the faster combustion rates when hydrogen was added to the natural gas. Understanding the effect of fuel change in existing systems can provide insight on utilizing hydrogen and natural gas mixtures as the primary fuel without the need for major changes in the engine.