According to the national rail operator, KORAIL, the locomotive and four of the train's seven carriages jumped the tracks near Yulchon station, some 330 kilometres (200 miles) south of Seoul.
The train was carrying 27 people, including two locomotive engineers, one of whom was killed in the accident.
Yonhap news agency quoted police as saying the train was rounding a bend at 127 kilometres per hour, when it should have been moving at less than 50kph.
The second engineer was reportedly in a serious condition, while another seven people suffered mostly minor injuries.