In 1943–1945 the family lived in New York City where she studied composition with Vittorio Giannini at the Juilliard School of Music.
She gave several solo recitals and performed with the Iceland Symphony Orchestra, for example in concertos by Mozart, Beethoven, and Schumann, as well as her own composition, Slátta (1977).
She was awarded the Order of the Falcon, Knight's Cross class (Riddarakross), for accomplishments in music.
[1] Jórunn Viðar has written a number of compositions based on Icelandic folk songs.
She also composed music for the film Síðasti bærinn í dalnum (The last farm in the valley).