The paper considers a staged conversion process of pulverized coal fuel in the MHPS-type gasifier, which uses mixtures of oxygen and carbon dioxide as a gasifying agent instead of air. Similar conversion processes can be applied in the process diagrams with the capture and disposal of carbon dioxide. The research tool is a reduced-order mathematical model of coal particles' conversion in a reacting gas flow. Replacement of nitrogen with carbon dioxide leads to significant changes in the gasification process characteristics: the average reaction temperature decreases, but this decrease is partially compensated by an increase in the concentration of gaseous reactants. Thus, the gasification process efficiency and the fuel conversion degree increase. Calculations make it possible to identify a range of parameters with the highest cold gas efficiency values. The influence of oxygen concentration is estimated, the dependence of the fuel conversion degree on the reaction temperature is analyzed.