Grgić 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); Mali i veliki (Le Petit et le grand) (1966); Muzikalno prase (The Music Pig) (1966), winner of the Palme d'or at Cannes Film Festival, the 1968 shorts Tolerance and Suitcase as well as Ptica i crvek (The Bird and the Worm) (1977).
Grgić 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.
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