The carbon capture technology (CCT) is widely studied to decrease carbon emissions and improve the global climate. Supersonic separation is becoming a new strategy for decarbonization. In order to simulate the non-equilibrium condensing flow of CO2 in the supersonic nozzle more accurately, the mathematical model is modified and verified, and non-equilibrium condensation of carbon dioxide in different states and different inlet superheat levels are analysed numerically. In order to improve the separation efficiency of the supersonic decarbonization technology and reduce the energy loss, the nozzle structure is appropriately designed and optimized. Firstly, the model is verified by gas properties, different droplet growth models and surface tension models. The result shows that the real gas model can predict the non-equilibrium condensing flow in the nozzle more accurately than the ideal gas model. Among the four droplet growth models, the most suitable one was selected in order to predict the non-equilibrium condensation properties of CO2. The droplet surface tension is corrected by introducing temperature and the droplet radius, and the droplet condensation process is enhanced. Secondly, the condensing flow through the nozzle is predicted in different states (subcritical, near-critical and supercritical). The result shows that the prediction based on the modified model is basically consistent with experimental data. Analysing the predicted Wilson line, it is found that the non-equilibrium effect of the flow is quite different at different inlet conditions. The condensation locations gradually approach the nozzle throat, the condensation interval narrows with an increase in pressure, and the peak of the nucleation rate increases gradually. Furthermore, the effect of inlet superheat on the non-equilibrium condensing flow is investigated. As the temperature rises, the flow loss decreases and the thermal efficiency increases from 61.15% to 67.62%. Finally, four nozzles with different convergence shapes are calculated. One of them demonstrates stronger stability, lower losses and the highest thermal efficiency which is about 67.64%. Additionally, when the expansion angle is 7°, the average of the liquid mass fraction is the highest, about 21.7%.