  In this work, we study the chiral and deconfinement phase transitions in a
two-flavor Polyakov loop extended Nambu--Jona-Lasinio (PNJL) model. And note
that the self-consistent mean field approximation is employed by introducing an
arbitrary parameter $\alpha$ to measure the weights of the Fierz-transformed
interaction channels. By making use of this model, we systematically
investigate the chiral and deconfinement phase transition lines (as well as the
chiral ones in the NJL model for comparison) under different values of
$\alpha$. It is found that, the increasing of $\alpha$ helps to enhance the
chiral (pseudo)critical temperature at fixed chemical potential, and also to
enhance the chiral (pseudo)critical chemical potential at fixed temperature.
And the critical end point (CEP) vanishes when $\alpha$ becomes large enough.
Besides, we find that the incorporation of Polyakov loop increases $T_{CEP}$
but does not change $\mu_{CEP}$ for small values of $\alpha$.
