Climate change and environmental degradation pose a threat to Europe and the world. The mechanism that will address these challenges is the European Green Deal, which envisions transforming the EU into a modern, resourceful, economical and competitive economy, aiming for zero greenhouse gas emissions. Landfill gas generated in a landfill waste deposit poses a threat to the environment and people. In this aspect, its capture, treatment and safe neutralization or use for energy purposes are important. Treatment of landfill gas, which is the fuel for gas engines in cogeneration units, is crucial for their proper operation and the quantity and quality of electricity and heat generated. The purpose of this study was to perform research to determine the hydrogen sulfide content of landfill gas and the actual efficiency of hydrogen sulfide removal from the gas using activated carbon. The tests performed constitute the basis for the reliable operation of gas engines in cogeneration installations and are dedicated mainly to the operators of these installations. Accordingly, three measurement campaigns were carried out, each with 42 measurements, the first for the “raw” gas obtained directly from the landfill, the second for the gas before entering the carbon filter and the third after its treatment. In addition, surface analysis was performed, and the elemental composition of the “fresh” molded activated carbon constituting the filter material was determined using a scanning electron microscope with an EDS system. The results showed a high elemental content of carbon in the test sample at 92.78%, while the efficiency of hydrogen sulfide removal from landfill gas by activated carbon, calculated from the measurements, was 97.05%. The obtained test results confirmed the validity of using impregnated activated carbon to remove hydrogen sulfide from landfill gas and its high adsorption efficiency, which can consequently result in reliable operation of the gas engine in the cogeneration unit and ultimately fit in with the objectives of the European Green Deal. The research results are an incentive for operators of cogeneration installations to systematically examine the quality of landfill gas and the efficiency of biogas purification devices.