Born in Belišće, Osijek-Baranja, Ljubek competed in four Summer Olympics where he won four medals. This included two golds (C-1 1000 m: 1976, C-2 500 m: 1984 with Mirko Nišović), one silver (C-2 1000 m: 1984 with Mirko Nišović), and one bronze (C-1 500 m: 1976). His trainer was Laszlo Hingl. He also won ten medals at the ICF Canoe Sprint World Championships with four golds (C-1 1000 m: 1978, C-2 500 m: 1982, 1983; C-2 10000 m: 1985), three silvers (C-1 10000 m: 1981, C-2 1000 m: 1982, 1985), and three bronzes (C-1 10000 m: 1975, 1978; C-2 1000 m: 1983).