For the solution of air pollution caused by internal combustion engine vehicles, many countries have encouraged the usage of electric vehicles (EVs). However, by allowing more EVs without smart charging control or proper power grid operational strategies, undesirable problems related to the power grid operation may occur. The purpose of this paper is to evaluate the impact of EVs on radial distribution networks with residential and commercial loads based on Jeju island, the largest island in the coast of Korea. A probabilistic approach was used to determine EV charging demand. This study considered various variables affecting the EV charging demand such as charging starting time, initial state-of-charge of a battery, and EV battery charging characteristics. The total power demand and voltage deviation in the distribution systems were generated by a back/forward sweep method for a power flow analysis, and the energy losses on distribution networks were analyzed. The simulation results of this study showed that the power peak demand on the distribution systems can increase up to 60%, the system voltage can fall below 6.6% during the evening, and their energy losses can increase up to 66% because of 40% EVs penetration among the total vehicles in the studied cases.