A numerical study is conducted to understand better the flame structure in a CH4-O-2/N-2/CO2/H2O counter-flow diffusion flame with various mole fractions of CO2 and H2O. Special interest is focused on the thermal, chemical, and diffusion effects of these species on the flame temperature and emission index of CO (EICO). A key result of the study is that the flame temperature is significantly reduced because of the chemical and thermal effects of CO2. However, H2O has a minor effect on the flame temperature, because its chemical effect almost cancels out its thermal effect. Meanwhile, the chemical effect of CO2 induces the EICO to increase noticeably, although other effects of H2O and CO2 slightly decrease it. The diffusion effect of CO2 only affects the distributions of the flame temperature and major species. Moreover, the pathways of fuel oxidation reactions are also investigated, and it is found that the low-temperature hydrocarbon reaction pathway (C-1 branch) becomes more active under oxy-fuel combustion conditions.