She started her career at 17, when she temporarily performed as a singer of the Malihini Hawaiians pop quartet.

Together they won the Eurovision Song Contest 1963 representing Denmark with the jazz waltz "Dansevise" (Dancing tune) with music by Otto Francker and lyrics by Sejr Volmer-Sørensen.

She dropped out in the preliminaries, but the song's English version, written by Johnny Mercer in 1966 and sung by Frank Sinatra, became an international hit.

As a solo singer, Grethe participated in several Danish pre-selections for the Eurovision Song Contest, unsuccessfully.

Notably, in 1979 she entered the Dansk Melodi Grand Prix with Bjarne Liller and the song "Alt er skønt", which tied for equal first at the end of the voting but placed second after a re-vote.