Annan Thambi is the story of twin brothers, Appu and Achu. Appu is a talkative conman who always finds himself in trouble. While Achu, a mute, is nicer than his brother, he draws a dagger on Appu due to misunderstandings created by the villain Govindan, who is masquerading as his friend. Their father Ravunni, a ballet artist, separates them due to sibling rivalry, and Appu is sent to live with relatives in Pollachi.
He grows up to be a lovable thug who falls for Thenmozhy, while Achu marries Lakshmi. But soon major misunderstandings created by their enemies crop up and the brothers are baying for each others blood. Just before the climax, they come to the realization that others were behind their enemity, so they patch up their differences and take on their foes.