This study focuses on evaluation of the effectiveness of an afterburner designed for solid oxide fuel cells (SOFC) located upstream of a gas turbine. The afterburner plays an important role in a hybrid marine power system, which includes solid oxide fuel cells and a gas turbine (SOFC-GT), aimed at maximizing the utilization of exhaust gas heat and enhancing overall system efficiency. The research involves theoretical investigations into the burning process of residual combustible components in the exhaust gases of fuel cells within an ejector-type afterburner. By conducting three-dimensional calculations using a model of turbulent reacting flows, the study identifies key directions for improving the afterburner’s efficiency under conditions of low calorific value of the exhaust gases. The proposed design of the afterburner will ensure complete burnout of fuel residues after the fuel element stacks with minimal emissions of toxic components. The design is quite universal and does not require expensive catalysts. The calculations underscore the feasibility of utilizing the proposed combustion technology in marine SOFC-GT power systems. The results obtained pave the way for scientifically grounded strategies to improve the efficiency of future power systems integrating fuel cells and gas turbines, deepening our understanding of exhaust gas after burning processes. This knowledge will facilitate the development of highly efficient decarbonized power systems suitable for both marine and stationary applications.