Livadić was born in Celje, in present-day Slovenia.
A leader of the 19th-century Croatian national revival, he wrote the tune for Još Hrvatska ni propala, the anthem of the Illyrian movement. He frequently invited many of the movement"s most important members, together with such European celebrities as Franz Liszt, to his property at Samobor. He also composed numerous art songs in Croatian, Slovenian, and German, as well as marches, dances and scherzi for piano.
Probably the best of these piano works is a Nocturne in F sharp minor.
His work prepared the way for the nationalist Croatian composers Vatroslav Lisinski and Ivan Zajc. He died, aged 79, in Samobor.