In 1940, Barcza took third place, behind Max Euwe and Milan Vidmar, at Maróczy Jubiläum in Budapest. In September 1942, he took sixth place at the first European Championship in Munich; the event was won by Alexander Alekhine. In 1948, he took second place in Karlovy Vary; the event was won by Jan Foltys. In 1948, he tied for second/third place in Venice; the event was won by Miguel Najdorf. In 1950, he tied for second/fourth place in Salzbrunn (Szczawno Zdrój); the event was won by Paul Keres. In 1952, he took fifteenth place in Saltsjöbaden (interzonal). In 1957, he won in San Benedetto del Tronto. In 1961, he took third place in Vienna. In 1962, he tied for third/sixth place in Moscow. In 1962, he tied for fourteenth/fifteenth place in Stockholm (interzonal).
Barcza is remembered for the opening 1.Nf3 d5 2.g3, known as the Barcza System. Harry Golombek once said of Barcza, "[he] is a most versatile player in the openings. He plays g2–g3 sometimes on the first, sometimes on the second, sometimes on the third, and sometimes not until the fourth move."