He graduated from the Faculty of Mechanical Engineering, University of Kragujevac, and was employed in the car factory Zavodi Crvena Zastava (ZCZ) at the production, technology and maintenance sector in 1972 .
When he left ZCZ in 1977, he took up position as General Manager Assistant in charge of technical services sector at the Medical Center Dr Mihailo Ilic.
Almost ten years after, he returned to ZCZ as manager of one of the Car Assembly’s sectors in 1986. The following year he was appointed the Production Sector Manager, and soon afterwards the Car Assembly Manager.
One of the highlights of political career of Veroljub Stevanovic was when he became Member of the National Assembly of the Republic of Serbia from 1993 to 2001. At the same time, he was Member of the Council of the Republics of the Federative Republic of Yugoslavia Assembly from 1997 to 2001.
He was co-minister of industry in the transitional Government of the Republic of Serbia in 2000.
Of course, the citizen’s of Kragujevac remember him the best as the first voted democratic mayor of the city of Kragujevac in the office from 1996 to 2001.
On the first direct mayoral elections in 2004, he was again elected mayor.
At the local elections held on May 11, 2008, he was bearer of the electoral list Veroljub Verko Stevanovic (G17 and Together for Kragujevac) -Veroljub Verko Stevanovic, that won 43 306 votes, which brought 41 mandates of the member of the City of Kragujevac Assembly.
At the City Assembly session held on May 11, 2008, Stevanovic was elected Mayor for the third time by majority of votes from total of 87 members of the Assembly.
After the parliamentary elections held on May 11, 2008, Stevanovic became Member of the Serbian National Assembly.