  We investigate the chiral restoration and deconfinement phase transitions
under external magnetic field in frame of a Pauli-Villars regularized PNJL
model. A running Polyakov loop scale parameter $T_0(eB)$ is introduced to mimic
the reaction of the gluon sector to the presence of magnetic fields. It is
found that a decreasing $T_0(eB)$ with magnetic fields can realize the inverse
magnetic catalysis phenomena of chiral condensates of $u$ and $d$ quarks,
increase of Polyakov loop and the reduction of (pseudo-)critical temperatures
of chiral restoration and deconfinement phase transitions.
