The objective of the present study is the parametric investigation of a ground source heat pump for space heating purposes with boreholes. The working fluid in the heat pump is CO2, and the geothermal field includes boreholes with vertical heat exchangers (U-tube). This study is conducted with a developed model in Engineering Equation Solver which is validated with data from the literature. Ten different parameters are investigated and more specifically five parameters about the heat pump cycle and five parameters for the geothermal unit. The heat pump’s examined parameters are the high pressure, the heat exchanger effectiveness, the temperature level in the heater outlet, the flow rate of the geothermal fluid in the evaporator and the heat exchanger thermal transmittance in the evaporator. The other examined parameters about the geothermal unit are the ground mean temperature, the grout thermal conductivity, the inner diameter of the U-tube, the number of the boreholes and the length of every borehole. In the nominal design, it is found that the system’s coefficient of performance is 4.175, the heating production is 10 kW, the electricity consumption is 2.625 kW, and the heat input from the geothermal field is 10.23 kW. The overall resistance of the borehole per length is 0.08211 mK/W, while there are 4 boreholes with borehole length at 50 m. The parametric analysis shows the influence of the ten examined parameters on the system’s performance and on the geothermal system characteristics. This work can be used as a reference study for the design and the investigation of future geothermal-driven CO2 heat pumps.