Born Cornell Friedmann in Budapest, Hungary, Capa moved, at age 18, to Paris to work as his brother, Andre Friedmann's (Robert Capa), photo printer. In 1937, Capa moved to New York to work in the LIFE magazine darkroom. After serving in the U.S. Air Force, Capa became a LIFE staff photographer in 1946. The many Life covers that Capa shot included portraits of television personality Jack Paar, painter Grandma Moses, and Clark Gable.
In May 1954, Robert Capa, was killed by a landmine covering the early years of the Vietnam War. Cornell Capa joined Magnum Photos, the photo agency co-founded by his brother, the same year. For Magnum, Capa covered the Soviet Union, Israeli Six-Day War, and American politicians.
Beginning in 1967, Cornell Capa mounted a series of exhibits and books entitled The Concerned Photographer. The exhibits led to his establishment, in 1974, of the International Center of Photography in New York. Capa served for many years as the director of the Center. Capa has published several collections of his photographs including JFK for President, a series of photographs of the 1960 presidential campaign that he took for LIFE magazine. Capa also produced a book documenting the first 100 days of the Kennedy presidency, with fellow Magnum photographers, including Henri Cartier-Bresson and Elliott Erwitt.
Capa has authored forwards to several collections of his brother's photographs and is known to be protective of Robert Capa's memory and reputation. For example, when Robert Capa's famous image of a falling Spanish soldier during the Spanish Civil War was claimed to be a fake and not taken at 'the moment of death', Cornell Capa entered into a long battle to establish the legitimacy of the photograph, including tracking down the name of the soldier and his date of death.