  In this paper, for a Jacobi algebroid $A$, by introducing the notion of
Jacobi quasi-Nijenhuis algebroids, which is a generalization of Poisson
quasi-Nijenhuis manifolds introduced by Sti\'{e}non and Xu, we study
generalized complex structures on the Courant-Jacobi algebroid $A\oplus A^*$,
which unifies generalized complex (contact) structures on an
even(odd)-dimensional manifold.
