Addison Gerald Farmer (August 21, 1928, Council Bluffs, Iowa – February 20, 1963, New York City) was an American jazz bassist. He was the twin brother of Art Farmer.

Farmer was born an hour after his twin brother, on August 21, 1928, in Council Bluffs, Iowa, reportedly at 2201 Fourth Avenue.^[1][2] Their parents, James Arthur Farmer and Hazel Stewart Farmer, divorced when the boys were four, and their steelworker father was killed in a work accident not long after this.^{[3][4]: 443} Addison moved with his grandfather, grandmother, mother, brother and sister to Phoenix, Arizona when he was still four.^[5]: 1–3

Farmer and his brother moved to Los Angeles in 1945, attending the music-oriented Jefferson High School, where they gained music instruction and met other developing musicians such as Sonny Criss, Ernie Andrews, Big Jay McNeely and Ed Thigpen.^[6] The brothers earned money by working in a cold-storage warehouse^[1] and by playing professionally.

He took bass lessons from Frederick Zimmermann, and studied at Juilliard and the Manhattan School of Music.

By late 1945, Farmer was with Johnny Alston and His Orchestra recording for the Bihari Brothers' Modern Music label, backing Jeanne Demetz and, shortly after, on the Blue Moon label.^[7] Other band members for those recording dates included Al "Cake" Wichard and King Fleming. He later recorded with Teddy Edwards's band. Farmer played in several groups with his brother, including in ensembles led by Benny Golson and Gigi Gryce. He also played with Mose Allison, Jay McShann, Charlie Parker, and Miles Davis. He recorded extensively for Prestige Records.

Farmer died from sudden unexpected death syndrome on February 20, 1963, in New York City at the age of 34.

• Addison Farmer at Allmusic