Many of the synthetic refrigerants used in heat pump and air conditioning systems are potent greenhouse gases. In light of the increasing concern regarding climate change, there has been an increased interest in natural refrigerants such as carbon dioxide which have a comparatively negligible impact on climate change. Direct expansion geothermal heat pumps require a very large volume of refrigerant, making the use of a natural refrigerant particularly beneficial from an environmental perspective. In this study a numerical model has been developed to analyze the steady state performance of a direct expansion geothermal heat pump water heater using carbon dioxide in a transcritical cycle. The system incorporates a compressor, a counter-flow gas cooler, an expansion device and a ground heat exchanger which is the system evaporator. The model was developed by means of thermodynamic, heat transfer and fluid flow analysis of each component of the system. A comparison between predicted component performance and experimental results available in the literature indicated that the simulation can provide a reasonably accurate representation of an actual system. Given this verification, the simulation was used to gain an understanding of the direct expansion CO2 geothermal heat pump's performance under varying design and operating parameters. The salient parameters which were studied include: compressor speed, ground coil length, number of ground circuits and gas cooler length. The effect of monthly soil temperature variation was also investigated. The parametric study revealed several factors which are important for system optimization. First, at any given soil temperature an optimum mean evaporation temperature exists; even a small deviation from this optimum can have a significant impact on coefficient of performance. Another important factor is the number of evaporator circuits. Finally, the gas cooler and evaporator capacities were shown to have a large impact on performance; heat exchanger capacities should be matched for optimum performance. Utilizing the findings of the study, an optimized system was simulated and compared to the baseline. The optimized system achieved a coefficient of performance of 2.58, representing an 18% improvement over the baseline system. Heating capacity increased 17% to 12.3 kW. The study suggests that with further research and optimization, carbon dioxide can perform well in a direct expansion geothermal heat pump and is a suitable replacement for more environmentally degrading refrigerants.