The development of the oxy-fuel porous media combustion technique not only takes advantage of the characteristics of porous media combustion, such as a relatively low lean-burn limit and small volume, but also dramatically facilitates carbon capture and storage. In this paper, a two-layer porous burner model is established, in which a two-temperature equation model is adopted for calculation purposes. Differences in combustion behaviour between oxy-fuel and air-fuel conditions are compared. The results show that the difference in physical properties between CO2 and air is the main reason for the significant variation of combustion behaviours under the conditions of oxy-fuel compared to air-fuel. The specific performance is lower combustion temperature and flame propagation speed. The temperature under oxy-fuel combustion conditions is 300 K lower than that under air-fuel combustion conditions at an equivalence ratio of 0.6, and the stable range of oxy-fuel combustion is only approximately 50% of air-fuel combustion. The impact of porous media material parameters on combustion behavior has been investigated. These variables include the equivalence ratio, material thermal conductivity, volume heat transfer coefficient, and extinction coefficient, while the ratio of O2/CO2 remains fixed at 0.21/0.79. The influence of these variables on the stable velocity range and temperature field is consistent, but a large difference in values occurs. Reducing the thermal resistance of the burner by adjusting the properties of the porous matrix can increase the velocity limit of stable combustion. However, even if the thermal conductivity and extinction coefficient are increased by 5 times, there will be no significant impact on the stable range. Reducing the pore size of the combustion zone by 50% will increase the stable range by over 100%.