Tällberg, who started for the club Bollnäs Gymnastik och Idrottsförening (Bollnäs GIF), began his international career in the Four Hills Tournament in 1985/86 after he became Swedish champion on the large hill in 1985. On December 30, 1985 he jumped for the first time in Oberstdorf in the Ski Jumping World Cup . The first few years he remained unsuccessful on the tour. At the Nordic World Ski Championships in 1987 in Oberstdorf, he reached 46th place on the normal hill and 63rd place on the large hill.
At the 1988 Winter Olympics in Calgary , Tällberg jumped from the normal hill to 36th place and from the large hill to 22nd place, which he had to share with Remo Lederer . In team jumping he finished seventh together with Anders Daun , Jan Boklöv and his brother Staffan Tällberg . In his first competition after the Games in Meldal , Norway , he achieved 4th place for the first time among the top ten. In the following two seasons he could only jump into the points once on the large hill in Planica . At the ski flying world championship in 1990 in Vikersund he reached the end of the 11th place.