Let A be a Banach algebra and let f : $A{ imes}A{ ightarrow}A$ be an approximate bi-derivation in the sense of Hyers-Ulam-Rassias. In this note, we proves the Hyers-Ulam-Rassias stability of bi-derivations on Banach algebras. If, in addition, A is unital, then f : $A{ imes}A{ ightarrow}A$ is an exact bi-derivation. Moreover, if A is unital, prime and f is symmetric, then f = 0.