Kosta Cavoski was born on 26 October 1941 in Banatsko Novo Selo, district of Pancevo. His father was Sava, local physician and his mother Vera, born Ilic. He started the four year elementary school in Novi Sad, and finished it in Kovin, where he took up lower secondary school which he completed in Vrsac. He also finished high school in Vrsac in 1960.
He enrolled the University of Belgrade Law School in 1960 and graduated on 29 June 1964 with average grade 9.85. He became Bachelor of Science in 1969 with the thesis "The role of the US Supreme Court in the development of federal system". In 1973 he took his PhD thesis "The idea of freedom and democracy" which was later published under its real title "The possibilities of freedom in democracy".
In his youth as a high school student he accepted as true that communism was a promising future, so in 1959 he became a member of the League of Communists of Yugoslavia and took part in voluntary work projects five times (1958-1962), twice as a brigade commander (1959 and 1960). Each time he was honored as the best worker. During his studies in Belgrade he was a party and students' organization official and after graduation he was a professional official of the Students' Association of Yugoslavia and the Youth Association of Yugoslavia for three years. For nearly two years (1965-1967) he was a vice chairman of the Students' Association of Yugoslavia in charge of international relationships and in that capacity took part in numerous international gatherings including the congresses of the International Students' Conference in Nairobi 1966 and of the International Students' Union in Ulan Bator 1967. At the beginning of 1967 he resigned his position and after the big students' demonstrations in June 1968 he publicly renounced communism.
He began his academic career in 1970 as an assistant teacher at the Law School in Belgrade. This career was abruptly discontinued when at the beginning of 1973 he was first sentenced of alleged false information propaganda (the pretext for the sentence was an article published in "Gledista" magazine, issue 5-6/1972 titled "Which values are protected by our laws?") to five months of prison, two years on parole, and then on 31 December 1975 expelled from the Law School on the grounds of the so called moral and political inadequacy, which was established by a report signed by professors Dr. Jovan Djordjevic, Dr. Radomir Lukic and Dr. Pavle Dimitrijevic. He was without any job for two years and then was given position at the Institute for Comparative Law on 1 April 1978, where he stayed for ten years. At the end of 1988 he takes position at the Institute for Philosophy and Social Theory. As of 1 January 1990 after 15 years of absence, he started working again at the University of Belgrade Law School as a full time teacher.
Starting from 1968 he became a fierce critic of the regime, and then the so called dissident who was persecuted for years and two times arrested and detained for short. While Tito was still alive, from 1976 to 1979 he wrote a book titled "Tito – technology of power". After the trial to the so called "Belgrade six" in 1984 he became a member of the "Board for protection of thought and expression" and in 1989 he was among the founders of the Democratic Party.
Beside teaching at the Law School in Belgrade he also teaches at the Law School at the University of Srpsko Sarajevo, initially in Ilidza and then in Pale, since it was established at the end of 1994. At the beginning of 1996 the President of Republika Srpska appointed him a senator. He is the Chairman of the International Board for the truth about Radovan Karadzic since its establishment. Since 30 October 2003 he is a correspondent member of the Serbian Academy of Arts and Sciences.