A simulation on the performance of a transcritical $CO_2$ heat pump system is carried out to investigate its characteristics for various operating conditions. Cycle simulation models are established for a steady-state simulation and are verified by comparing experimental data. Based on correlations and methods available in the literature, the processes in individual components of the transcritical cycle are simulated to analyze the performance of $CO_2$ transcritical heat pump system. The simulation models are good enough to predict the performance of a $CO_2$ transcritical cycle. Simulation results are provided to show the relative effects when varying the size of internal heat exchanger and the discharge pressure of a compressor.