The T-50B plane went down at 10:28 a.m in Hoengseong, about 55 miles from Seoul, Yonhap News Agency reported.
Its pilot, identified only as Capt. Kim, 32, is believed dead, officials said.
Witnesses in the area said two planes that took off from an air base in nearby Wonju at 10:23 a.m and flew in parallel before one of them went down in flames.
The plane belonged to the Air Force aerobatic team, known as "Black Eagles."
The cause of the crash is not yet known.