  We investigate the convergence behaviors of the scalar and the vector
perturbations for a big bounce phase in loop quantum cosmology. Two models are
discussed: one is the universe filled by a massless scalar field; the other is
a toy model which is radiation-dominated in the asymptotic past and future. We
find that the behaviors of the Bardeen potential of the scalar mode near both
the bounce point and the transition point of the null energy condition are
good, moreover, the unlimited growth of the vector perturbation can be avoided
in our bounce model. This is different from the bounce models in pure general
relativity. And we also find that the maximum of an observable vector mode is
inversely proportional to the square of the minimum scalar factor $a_{bounce}$.
This conclusion is independent with the bounce model, and we may conclude that
the bounce in loop quantum cosmology is reasonable.
