  Using the concept of Jacobi-Lie group and Jacobi-Lie bialgebra, we generalize
the definition of Poisson-Lie symmetry to Jacobi-Lie symmetry. In this regard,
we generalize the concept of Poisson-Lie T-duality to Jacobi-Lie T-duality and
present Jacobi-Lie T-dual sigma models on Lie groups, which have Jacobi-Lie
symmetry. Using this symmetry, new cases of duality appear and some examples
are given. This generalization may provide insights to understand the quantum
features of Poisson-Lie T-duality, in a more satisfactory way.
