The Cayley graphs on the symmetric group plays an important role in the study of Cayley graphs as interconnection networks. Let $Cay(S_n, B)$ be the Cayley graphs generated by transposition-generating trees. It is known that for any $F \subset E(Cay(S_n, B))$, if $|F|\leq n−3$ and $n\geq 4$, then there exists a hamiltonian cycle in $Cay(S_n, B)−F$. In this paper, we show that $Cay(S_n, B)−F$ is bipancyclic if $Cay(S_n, B)$ is not a star graph, for $n\geq 4$ and $|F|\leq n−3$.