Feibusch served as a solder in the trenches on the Russian Front from 1916 to 1918. He began studying medicine in Munich, but then moved to the Academy of Fine Arts in Berlin in 1920, where he studied under Karl Hofer and became his master student. He travelled to Italy from 1921 to 1923 in order to study. He then stayed in Paris from 1923 to 1924 to study with Othon Friesz and André Lhote, and participated there in exhibitions of the Salon d’Automne and the Salon des Indépendants. Feibusch returned to Frankfurt am Main in 1925, and became a member of the Frankfurt Artists’ Association. In 1931, he was awarded the Great State Prize for painting. In 1933, Feibusch went into exile, emigrating to London.
He married Sidonie Cramer in 1935 and joined the London Group. But in Germany, his paintings were denounced, confiscated and destroyed. One of his paintings was confiscated from the City Gallery in Frankfurt am Main, and was shown in the “Degenerate Art” exhibition in 1937 in Munich. In England, Feibusch participated in the exhibition Twentieth-Century German Art in 1938. In Britain, Feibusch became one of the most important mural artists for churches, cathedrals and synagogues. In 1938, he was made a British citizen; his German citizenship was annulled in 1939. In 1946, after the Second World War, Feibusch published a book entitled Mural Paintings, a theoretical work about the formal rules and techniques of mural painting.
In 1967, the Federal Republic of Germany awarded him A First Class Cross of Merit. Feibusch went partially blind, and so turned to sculpting instead. In 1985, he was awarded an honorary doctorate by the Archbishop of Canterbury, and in 1989 he was presented with the Grand Cross of Merit by the Federal Republic of Germany.