Art Farmer was born in Council Bluffs, Iowa on August 21, 1928. When he was 4, his family moved to Phoenix, Arizona. Farmer learned to play the piano and violin when he was in elementary school. Later, when he joined his school marching band he was assigned to play the sousaphone. He also played the bugle at flag raising ceremonies. Farmer loved jazz and especially the sound of the trumpet. He liked to go see big jazz bands when they came to town. He started playing in a local dance band when he was 15.

Farmer’s brother Addison played bass. In 1945, he and his brother moved to Los Angeles. There Farmer started playing with LA based bands.