He won the 1974 Canadian Open Chess Championship.

In 1983 he was ranked third in the Elo rating list,[2] but he never succeeded in reaching the Candidates Tournament stage of the World Championship.

He played for Yugoslavia in twelve Chess Olympiads, nine times on top board, with an overall result of 63.5% (+66−22=75).

[3] Ljubojević tied for first place with Robert Hübner at Linares 1985.

[4] He has defeated almost every top grandmaster active during his career, including world champions Garry Kasparov,[5] Anatoly Karpov,[6][7][8] and Viswanathan Anand.