Vučković graduated from the University of Belgrade Faculty of Law in 1964 and took postgraduate studies in France and the United States of America.
He contributed to a law barring the League of Communists from operating through Serbia's labour organizations, and in 1990 he was one of only six delegates to vote against the adoption of a new constitution favoured by Milošević.
Milošević's Socialist Party of Serbia (Socijalistička partija Srbije, SPS) won a majority victory, and Vučković served as a member of the opposition.
He was a member of the foreign affairs committee and took part in delegations to the European Parliament and the Council of Europe, as well as to Greece and the Czech Republic.
[5] For the 1992 Serbian parliamentary election, Serbia abandoned single-member electoral divisions and adopted a system of proportional representation.
He was also a co-founder of Serbia's Center for Democracy Foundation and Forum for International Relations in this period, and served for a time as vice-president of the latter organization.
[12][13] In 2000, the DC participated in the Democratic Opposition of Serbia (Demokratska opozicija Srbije, DOS), a broad and ideologically diverse coalition of parties opposed to Milošević's administration.
Vučković was given the 229th position; the list won thirty-seven mandates, and he was included in the DC's delegation when the new assembly convened in early 2004.