Hema (Telugu star Jaya Pradha, in her first Hindi film) plays a mute. Her stepmother and stepsister ill-treat her and scheme to get rid of her by fixing her marriage with an old man.

Hema runs away from home with Raju (Rishi Kapoor), a dafli (a kind of drum) player. They fall in love, but Hema feels she is unfit for him as she is dumb, while Raju feels he is unfit for her because he is poor and suffers from a disease. The couple try hard to survive and fulfil Hema's dream of becoming a great dancer.

Sargam is a remake of the Telugu movie, Siri Siri Muvva, directed by K Vishwanath in 1978. Jaya Pradha featured in the original as well; Telugu actor Chandramohan played the male lead.