Cryogenic CO₂ capture is considered as a promising CO₂ capture method due to its energy saving and environmental friendliness. The phase equilibrium analysis of CO₂-mixtures at low temperature is crucial for the design and operation of a cryogenic system because it plays an important role in analysis of recovery and purity of the captured CO₂. After removal of water and toxic gas, the main components in typical boiler gases are N₂/CO₂. Therefore, this paper evaluates the reliabilities of different cubic equations of state (EOS) and mixing rules for N₂/CO₂. The results show that Peng-Robinson (PR) and Soave-Redlich-Kwong (SRK) fit the experimental data well, PR combined with the van der Waals (vdW) mixing rule is more accurate than the other models. With temperature decrease, the accuracy of the model improves and the deviation of the N₂ vapor fraction is 0.43% at 220 K. Based on the selected calculation model, the thermodynamic properties of N₂/CO₂ at low temperature are analyzed. According to the results, a new liquefaction combined with a desublimation system is proposed. The total recovery and purity of CO₂ production of the new system are satisfactory enough for engineering applications. Additionally, the total energy required by the new system to capture the CO₂ is about 3.108 MJ·kg⁻¹ CO₂, which appears to be at least 9% lower than desublimation separation when the initial concentration of CO₂ is 40%.