According to the 5th national plan for electric power demand and supply, the 3rd HVDC link will be installed between KEPCO and Jeju Island system and go into operation in June, 2016. However, if it adopt LCC HVDC, Jeju power system could be in voltage instable condition. In order to solve the problem, we propose the application of VSC HVDC to the 3rd HVDC project. In the past, VSC HVDC has many disadvantages such as, inefficiency in conversion, size limit, and expensiveness, compared to LCC HVDC. Recently, the new technologies and the demand for renewable energy interconnection are leading a large growth in VSC HVDC market. In this paper, we will introduce the technical and market trends of VSC HVDC and power system stability analysis results for Jeju power system having LCC and VSC HVDCs.