In this study, a simulation model for a $CO_2$ heat pump using vapor injection was developed and validated. It was used to predict the improvement of the heating performance of the $CO_2$ heat pump at various operating conditions. The simulation results showed consistent results with the measured data. The heating performances of the vapor injection and non-injection heat pumps were compared by varying the outdoor temperature and compressor frequency. The heating capacity of the vapor injection heat pump was 40% higher than that of the non-injection heat pump at the outdoor temperature of $-8^{circ}C$. The performance of the vapor injection heat pump was consistently higher than that of the non-injection heat pump even when the compressor frequency was reduced to 35 Hz at the outdoor temperature of $-3^{circ}C$.