  The QCD phase transitions are investigated in the presence of an external
magnetic field in the Polyakov improved Nambu--Jona-Lasinio (PNJL) model. We
detailedly analyze that how the filling of multiple Landau levels by light (up
and down) quarks deforms the QCD phase structure under different magnetic
fields. In particular, we concentrate on the phase transition under a magnetic
field possibly reachable in the non-central heavy-ion collisions at RHIC. The
numerical result shows that two first-order transitions or more complicate
phase transition in the light quark sector can exist for some magnetic fields,
different from the phase structure under a very strong or zero magnetic field.
These phenomena are very interesting and possibly relevant to the non-central
heavy-ion collision experiments with colliding energies at several $A$ GeV as
well as the equation of state of magnetars. Besides, we investigate the entropy
oscillation with the increase of baryon density in a magnetic background.
