Grbić graduated from the Academy of Performing Arts in Sarajevo at the University of Sarajevo, where he earned MA Degree in Acting. Since 1996 he has performed in more than 60 theater plays on the main stage of the Sarajevo National Theatre. He starred in almost 40 Feature films in Bosnian, Croatian, German, Austrian, Italian, Irish, Polish, Turkish, Macedonian, Australian, Canadian and US productions. He starred as Bogdan in Mission: Impossible – Ghost Protocol, where he performed opposite Tom Cruise. Grbic starred in television shows such as Ruža vjetrova, Lud, zbunjen, normalan, Gang Related and Viza za budućnost. He has lived in Los Angeles since 2013.