Because of its high dependence on fossil fuels, the South Korean government has consistently endeavored to use renewable energy sources to operate power generation systems. The South Korean government has advised local communities and governments of the islands to establish independent renewable power generation systems, particularly since the installation, operation, and management of power generation systems to connect the islands to the electricity grids amount to large costs. As such, this study explores potential solutions for establishing independent renewable power generation systems in Gadeokdo Island, one of the largest islands in South Korea, by using the HOMER software. The simulation results show that wind turbines, PV panels, converters, and batteries can be used to operate the power generation systems for Gadeokdo Island. The current study presents an optimal renewable power generation system within the framework of the cost of energy (COE), renewable fraction, and total net present cost (NPC). The system achieves $0.326 per kWh of COE and 1.00 of renewable fraction. Both implications and limitations of the proposed system are discussed.