Studying closed gas turbine cycles on supercritical carbon dioxide is currently a promising issue in the development of power energy sector in terms of increasing energy efficiency and minimizing greenhouse gas emissions into the atmosphere. Combustion of methane with oxygen in the combustion chamber occurs not in the nitrogen environment, but in the environment of carbon dioxide, that is the working fluid of the cycle, which is an inhibitor of chemical reactions. A large mass content of such a diluent of the reaction mixture in the volume of the chamber leads to the risks of significant chemical underburning, efficiency decrease of the combustion chamber and the cycle as a whole. The aim of the research is to study the kinetic parameters of the combustion of methane with oxygen in a supercritical CO2 diluent medium to ensure reliable and stable combustion of fuel by assessing the degree of the inhibitory effect of CO2 and determining its permissible amount in the active combustion zone of the combustion chamber. The research method is a numerical simulation of turbulent-kinetic processes of methane combustion in the combustion chamber using the reduced methane combustion mechanism. Ansys Fluent software package has been used. The authers have studied the impact of CO2 diluent on fuel cоmbustion in methane-oxygen combustion chambers. It is found that the combustor flame stabilization takes place if the content of СО2 diluent supplied to the mixture with oxidizer is 0,46–0,5 of mass fraction; additional СО2 diluent forms local low temperature zones which slow down the combustion process. When this happens, adding cooling СО2 into the flame stabilization zone should be eliminated. The study has found that no more than 20 % of the total carbon dioxide content should be supplied to the combustion chamber; to stabilize the flame and reduce its length, it is necessary to install blades to swirl the fuel and oxidizer mixed with CO2 at the inlet of the combustion chamber; CO2 supply for cooling should be carried out not less than 130 mm away from the burner mouth.