Chien (played by Jackie Chan), an orphan adopted by a kung-fu school, is overworked as their janitor and abused by the kung fu teachers as a walking punching-bag. Chien befriends an old beggar (Yuen Siu Tien) by offering him a meal and a place to stay. Unknown to Chien, the old beggar is actually the last surviving master of the Snake-style of kung fu. The old man is on the run from the Eagle Claw clan, which is viciously killing off all of the rival Snake-style kung fu masters. Seeing that Chien is being abused, the old man gives Chien kung fu lessons so he can defend himself.

The old man leaves the school to find a better hiding spot. Chien later finds him and the old man agrees to give him more lessons, on the condition that he does not call him "sifu" ("master"), since they are friends.

Chien practices the lessons and learns to avoid being hurt by the school's bumbling teachers. When the school is invaded by the Mantis school, Chien easily defeats their master using snake to everyone's amazement. Unfortunately, one of the passing wanderers who witnessed the fight was a master of the Eagle Clan.

Chien meets the Eagle Claw clan master, who inquires about the old beggar. The Eagle Claw master lies, saying that he was a student of the old beggar and asks Chien to help him find the old man. Realising that his Snake-style fighting is no match for the style practiced by the Eagle Claw master, Chien creates a new style from watching his pet cat kill a cobra.

Eventually, Chien unwittingly leads the Eagle Claw master to the old man. In the duel, Chien merges his "cat style" with snake style to finally defeat the Eagle Claw master. Chien announces that he will call his technique "Cat's Claw", but the Old man suggest that he give the technique the name "Snake in the Eagle's Shadow".