A hydrogen purification system with a supersonic nozzle pretreatment process is proposed to improve the performance of traditional CO2 removal processes from hydrogen-rich streams. A mathematical model of the H2–CO2 double-component condensation was established to investigate the feasibility of CO2 capture in a hydrogen-rich stream using a supersonic nozzle. Compared to the single-phase model, this model is more similar to the objective flow facts and can effectively correct the deviation of the single-phase flow model by 21.4%. Furthermore, the parameters in the H2–CO2 double-components spontaneous condensation process in the nozzle were analyzed, and the microscopic mechanism of CO2 spontaneous condensation was clarified. Finally, the effects of the inlet parameters on the carbon capture efficiency were analyzed. The results indicated that the nozzle is more suitable for purifying hydrogen-rich streams with low temperatures and high carbon content, confirming the possibility of using a supersonic nozzle as a carbon capture method.