The building sector is an energy-consuming sector, and the development of zero-energy buildings (ZEBs) is necessary to address this. A ZEB’s active components include a system that utilizes renewable energy. There is a heat-pump system using geothermal energy. The system is available regardless of weather conditions and time, and it has attracted attention as a high-performance energy system due to its stability and efficiency. However, initial investment costs are higher than other renewable energy sources. To solve this problem, design optimization for the capacity of geothermal heat-pump systems should be performed. In this study, a capacity optimization design of a geothermal heat-pump system was carried out according to building load pattern, and emphasis was placed on cost aspects. Building load patterns were modeled into hospitals, schools, and apartments, and, as a result of optimization, the total cost over 20 years in all building load patterns was reduced.