Prosecutors say Timothy Bradley erupted when cabin crew refused to serve him more alcohol during a British Airways flight from Phoenix, Arizona, to London.
Judge Richard McGregor-Johnson said Bradley was "thoroughly abusive" He said one crew member feared Bradley was going to attack him.
Bradley was arrested when the plane landed at Heathrow Airport on Aug. 20, and pleaded guilty to being drunk aboard a plane and common assault.
His lawyer said he was "totally and utterly ashamed" of his behavior.
The judge sentenced Bradley on Friday to three months for drunkenness and one month for assault, to run concurrently.