This paper proposes the installation of a new modular multilevel converter based high-voltage direct current (MMC-HVDC) system to connect between mainland and Jeju island power systems in Korea in 2020. The purpose is to combine with two old line-commutated converters (LCC)-based HVDC system to achieve a stability of the Jeju island power system. The operation of the overall system will be analyzed in three cases: (i) wind speed is variable, (ii) either one of the LCC-HVDC systems is shutdown because of a fault or overhaul, (iii) a short circuit fault occurs at the mainland side. The effectiveness of the proposed control method is confirmed by the simulation results based on a PSCAD/EMTDC simulation program.