Son of an artist (his father was an actor and director), Vajda started his career as editor (even though he also worked as artistic designer and writer) for different directors, such as Billy Wilder and Henry Koster. Eventually, he undertook his first directorial effort in his native country, Hungary.
Soon afterwards World War II, he established in Italy, where he directed two movies. Finally, he moved to Spain. During the 40s, Vajda directed several movies in Portugal, United Kingdom and, mainly, in Spain.
However, his artistic splendor would arrive in the 50s. Wajda's movies during this period are clearly influenced by German director Fritz Lang. His main works during this period are: The Miracle of Marcelino (aka Marcelino Pan y Vino) (1955), My Uncle Jacinto (1956), Afternoon of the Bulls (1956), The Man Who Wagged His Tail (1957) with Peter Ustinov, y It Happened in Broad Daylight (1958). They were both critically and public acclaimed: The Miracle of Marcelino and My Uncle Jacinto achieved different prizes in Cannes Film Festival and Berlin Film Festival; Afternoon of the Bulls was nominated for Palme d'Or and It Happened in Broad Daylight for Golden Bear.
During the 60s, Vajda worked on several different minor works in Germany and Spain. Finally, He passed away in Barcelona in 1965.