-With the current global need for eco-friendly energies, the large scale use of Electric Vehicles (EVs) is predicted. However, the need to frequently charge EVs to an electrical power system involves risks such as rapid increase of demand power. Therefore, in this paper, we propose a practical smart EV charging scheme considering a Time-of-Use (ToU) price to prevent the rapid increase of demand power and provide load leveling function. For a more practical analysis, we conduct simulations based on the actual distribution system and driving patterns in the Republic of Korea. Results show that the proposed method provides a proper load leveling function while preventing a rapid increase of demand power of the system.