Born in Zagreb, in the former Kingdom of Yugoslavia, Grgic was nominated for the Academy Award for Animated Short Film at the 52nd Academy Awards for his 1979 film Dream Doll, produced by Bob Godfrey. 
Grgic created the animated series Professor Balthazar for Zagreb Film and also animated 24 episodes of its series Maxi Cat (1971–73). His other credits include the 1965 animated shorts Peti and Đavolja Posla (The Devil's Work); Muzikalno prase (The Music Pig) (1966), winner of the Palme d'or at Cannes Film Festival, and the 1968 shorts Tolerance and Suitcase.
Grgic was asked to join the National Film Board of Canada (NFB) after producers saw his film Scabies. He directed and animated three shorts with the NFB: Hot Stuff (1971), named best educational film at the Zagreb World Festival of Animated Films, Who Are We? (1974) and Deep Threat (1977). 
He has an award named after him at the Zagreb World Festival of Animated Films: the Zlatko Grgić Prize for best first production apart from educational institutions.
- "Cartoons Considered For An Academy Award – 1979 -". cartoonresearch.com.
- "Zlatko Grgic". theoscarsite.com.
- Mazurkewich, Karen. Cartoon Capers: The Adventures of Canadian Animators (Excerpted in Canadian Animation Resources). McArthur & Co. p. 57. ISBN 978-1-55278-093-0. Retrieved 15 December 2011.
- "Cartoons Considered For An Academy Award 1975 -". cartoonresearch.com.
- "20th WORLD FESTIVAL OF ANIMATED FILM – ANIMAFEST ZAGREB 2010 SHORT FILM COMPETITION REGULATIONS" (PDF). Retrieved 2015-03-22.
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