Being sportsman himself, Bošković got involved in Montenegrin handball in 2005 when he became a board member of the Women's Handball Club, Budućnost.
In December 2006 he became the president of the club.
After his election, he set the European Champions League title as a medium-term goal.
Starting from his election, all the decisions were made keeping this goal in mind, for which general public criticized him quite often.
On May 13, 2012 WHC "Budućnost" won its first European Handball Federation Champions League (EHFCL) title.
Prior to this historical triumph, the club lost seven EHFCL semifinals.
During Boskovic's presidency the club also won the second Champions League title in 2015, eleven domestic championships (2007-2017), six regional league titles (2010-2015), one Cup Winner's Cup (CWC) title in 2010 and was also the semifinalist of the EHFCL in 2011, 2016 and 2017  and the finalist in 2014.

Due to obligations in EHF, Boskovic resigned as president of Handball Club Buducnost on March 12, 2018.

In 2011 he was the elected president of the Montenegrin Handball Association  and held this position until September 2016 when he stepped down due to the candidacy for the vice-president of the European Handball Federation.
In 2012 both men's and women's national teams accomplished the best results in their history.
 The men's national team qualified for the World Handball Championship, that was held in Spain in 2013 Few months after that, on August 11, women's national team won the silver medal at the London 2012 Olympics.
This medal is viewed as a historical achievement since it is the first Olympic medal for Montenegro since its independence in 2006.
The great year for Montenegrin handball was crowned with the European Championship title which Montenegrin Women's Handball Team won on December 16, 2012.

Many analysts and organizations, including the International Handball Federation (IHF), agree that Bošković is one of the people who have contributed the most to the immense success of the Montenegrin handball.
The IHF even referred to him as the "father of success".
Recognizing his stellar work, the European Handball Federation (EHF) elected Mr. Boskovic as an Executive Committee (ExeC) Member in June 2012.
Furthermore, he was elected as the EHF Vice President and IHF Council Member in November 2016.
Being sportsman himself, Bošković got involved in Montenegrin handball in 2005 when he became a board member of the Women's Handball Club, Budućnost. In December 2006 he became the president of the club. After his election, he set the European Champions League title as a medium-term goal. Starting from his election, all the decisions were made keeping this goal in mind, for which general public criticized him quite often. On May 13, 2012 WHC "Budućnost" won its first European Handball Federation Champions League (EHFCL) title. Prior to this historical triumph, the club lost seven EHFCL semifinals. During Boskovic's presidency the club also won the second Champions League title in 2015, eleven domestic championships (2007-2017), six regional league titles (2010-2015), one Cup Winner's Cup (CWC) title in 2010 and was also the semifinalist of the EHFCL in 2011, 2016 and 2017  and the finalist in 2014.
Due to obligations in EHF, Boskovic resigned as president of Handball Club Buducnost on March 12, 2018.
In 2011 he was the elected president of the Montenegrin Handball Association  and held this position until September 2016 when he stepped down due to the candidacy for the vice-president of the European Handball Federation. In 2012 both men's and women's national teams accomplished the best results in their history.  The men's national team qualified for the World Handball Championship, that was held in Spain in 2013 Few months after that, on August 11, women's national team won the silver medal at the London 2012 Olympics. This medal is viewed as a historical achievement since it is the first Olympic medal for Montenegro since its independence in 2006. The great year for Montenegrin handball was crowned with the European Championship title which Montenegrin Women's Handball Team won on December 16, 2012.
Many analysts and organizations, including the International Handball Federation (IHF), agree that Bošković is one of the people who have contributed the most to the immense success of the Montenegrin handball. The IHF even referred to him as the "father of success". Recognizing his stellar work, the European Handball Federation (EHF) elected Mr. Boskovic as an Executive Committee (ExeC) Member in June 2012. Furthermore, he was elected as the EHF Vice President and IHF Council Member in November 2016.
Predrag Bošković