This paper presents a theoretical investigation on the thermal performance of a natural refrigerant-based cascade refrigeration-heat pump system used to produce both heating and cooling. A parametric evaluation is also presented for carbon dioxide-propylene working pair by varying parameters like evaporating, gas cooler exit temperature, and temperature difference in the cascade heat exchanger of the system. The topping cycle of the system is provided with a vortex tube instead of an expansion valve. The maximum increase in coefficient of performance of the present system is 5.9 % compared to that of the transcritical cascade cycle without vortex tube expander, in the assumed range of operating parameters. The model predicts performance parameters and operating conditions e.g., pressure, enthalpy, temperature, and entropy at different state points. The proposed transcritical model is optimized for overall coefficient of performance, intermediate temperature, and mass flow ratio with the help of multi-linear regression analysis. The influences of main parameters on the optimum design quantities are displayed in tables and figures. The cascade refrigeration-heat pump model with carbon dioxide/propylene as refrigerants is validated by comparing the coefficient of performance values with other reference cascade systems. This study could contribute to the further development and the optimal design of carbon dioxide-propylene cascade refrigeration systems.