Apparently, it used to be sung to the tune of Auld Lang Syne, but the music was changed in 1937.
"First performed in 1896, it was well-known by all Koreans by 1910. (It was not the national anthem at this time however, as an imperial anthem was in use at the time.) At this time, the song was usually sung to a Scottish folk song, "Auld Lang Syne", as well as occassionally to other music. In that year, the Japanese invaded Korea, and banned the anthem. However, it was still popular with Koreans abroad as a yearning for national independence.
In 1937 composer Ahn Eaktay wrote the music that's currently in use for the anthem (he wanted the song to have a Korean melody and not that of a folk song of a foreign nation). It was adopted by the government in exile and then, when South Korea was founded in 1948, three years after the Japanese occupation ended, it was officially adopted by that government."
http://www.nationalanthems.info/kr.htm
