His first international medal winning Csaba Fenyvesi at the World Fencing Championship in 1967, when he received the bronze medal behind the Soviet and the French team with the Hungarian epee team. At the 1968 Olympic Games in Mexico City Csaba Fenyvesi, Győző Kulcsár, Pál Nagy, Zoltán Pál Schmitt Nemere and won in the final against the Soviet team, which Kulcsár and Nemere had already won team gold in 1964.
After silver at the World Fencing Championship in 1969 behind the Soviet team in 1970 with the Hungarians Sándor Erdős, Fenyvesi, Kulcsár, Nemere and Schmitt won the World Cup final against the Poles. In the individual decision Fenyvesi won the bronze medal, it should be his only individual medal at World Championships. After the Hungarians had in 1971 defended her world title, they also won at the Olympic Games in Munich in 1972 the final, with the final victory for Erdős, Fenyvesi, Kulcsár, István Osztrics and Schmitt quite clear as was against the Swiss fencer with 8:4. In the final round in epee individual Fenyvesi had clearly won his first four fights, against Frenchman Jacques La Degaillerie enough for him at the end of a draw to Olympic victory, the Frenchman won silver before Kulcsár. Fenyvesi occurred also with the Hungarian foil team that narrowly lost the battle for the bronze medal against the French.
In the World Fencing Championship in 1973, the Hungarian epee team since 1969, was defeated for the first time at the season's climax in the final they lost to the team from the Federal Republic of Germany. 1974 was not one Fenyvesi the Hungarian team, but in 1975 he won the bronze medal with the team at the World Championships. At the Olympic Games in 1976 Fenyvesi reached with the sword team, the battle for the bronze medal, but was defeated there against the Swiss. In the individual and with the foil team he finished each case together with other seventh. His last major title, won the doctorate dentist at the World Fencing Championship in 1978, when he again won team gold along with Kulcsár and Osztrics and Ernő Kolczonnay and Jeno Papp.