Győző Burcsa was born on the 13th March 1954 in Kaposvar. He made his first step in his career at his home town club. He helped them to second in division two behind Szeged, which ended up with Kaposvar being promoted to the first division for the first time in their history.

Kaposvar ended up in 13th place in their first season at the top level, with Burcsa scoring 11 goals in the majority of games that he played, making him the teams top goalscorer. This happened at the same time that Videoton were battling with Ferencvaros for the first division title. Vidi ended up in second place at the end of that season. Burcsa made the move to Szekesfehervar by the time that the following season kicked off. He quickly became a key player for the side. He stayed at the club for five years making 147 league appearances, scoring 57 goals. Having not won any silverware with the Fehervar side, it was no surprise when he made the move to Raba ETO, who were perhaps the best team of that era.

Burcsa won two titles during his time at ETO, as well as a runners up medal in his three years there. He picked up the Pro Urbe award in the autumn of 1983 while playing for the Győr club. He also played for ETO in the Hungarian cup final of 1984 against Siofok.

It was during that year that he returned back to Szekesfehervar, as a member of the legendary UEFA cup final side. The Videoton team of that 1984-85 season not only ended up in third place in the league, but made it all the way to the UEFA cup final. Győző Burcsa played in each of the 12 UEFA cup matches, missing just a single minute of that European campaign when he came off in the 89th minute in the game against Prague.

The next step in his playing career was a move to French side Auxerre in 1985. He spent two seasons with them, playing against AC Milan in the UEFA cup. Burcsa had a very famous team mate in France in the form of Erik Cantona, who went on to become a legend at Manchester United. There were also several French internationals at Auxerre with Jean Marc Ferreri and keeper Bruno Martini. He also played with the future Polish international manager Pawel Janas during his time in France. He then moved down to the lower leagues at Melun and RC d'Arras. Burcsa was a player manager with the latter side, where he finally ended his playing career.

Győző Burcsa made a total of 18 appearances for the Hungarian Olympic side, and a further 15 international caps from 1979 to 1987. He was a member of the 1986 World cup squad in Mexico, playing in two group matches in that competition.

He went on to manage three Hungarian clubs after his playing career came to an end. Burcsa managed Videoton from 1990-1992 before further spells at Nyiregyhaza and finally Sopron. He has been working for his own company business in recent years.