Kurt Leimer demonstrated musical talent from a young age. His great-uncle, Karl Leimer, was instructor to educator Walter Gieseking who together published several piano textbooks. His talent was recognized by Gieseking, Carl Schuricht, and Wilhelm Furtwängler who helped launch his career as a concert pianist. At the age of 18, he received a scholarship to the Berlin Conservatory, where he studied alongside Rachmaninov student Vladimir Horbowski and Winfried Wolf. The same year, 1938, Leimer made his concert debut in Berlin. In 1939, he continued his studies under Edwin Fischer.
During the latter stages of World War II, Leimer was drafted into the Wehrmacht and was imprisoned in Livorno. The wartime injuries of his peers inspired his most familiar work, the Piano Concerto for Left Hand. The work was inspired by a college friend who lost his right arm to a grenade injury. In 1953, Leimer and the Vienna Philharmonic premiered the work with Herbert von Karajan conducting. In 1955, he premiered his 4th Piano Concerto in C minor with Leopold Stokowski conducting at Carnegie Hall in New York.
Richard Strauss was a particular champion of Leimer's concert career; he dedicated his Panathenäenzug for piano and orchestra to Leimer. Leimer considered performing the premier of Strauss' work to be a highlight of his career.
- Piano Concerto for the left hand
- Piano Concerto in C minor
- Kurt Leimer and Herbert von Karajan conducting the Philharmonia Orchestra recorded the concerto in November 1954 in London, Kingsway Hall (Karajan Complete EMI recordings 1946-1984 vol. 1 CD 25).