  The effect of the anomalous magnetic moment (AMM) on the chiral restoration
is investigated at zero temperature in the strong magnetic fields with the
vacuum magnetic regularization scheme. It is shown that the chiral restoration
diagram sensitively depends on the AMM in the ultrastrong magnetic fields. In
our work, the parameterization of AMM is employed as proportional to the square
of the chiral condensate. The critical chemical potential is found to decrease
linearly by the increasing coefficient in the AMM scale. At a smaller scale of
the AMM, the critical chemical potential could go down and then grow up as the
magnetic field increases. But at a larger scale, the magnetic catalysis on the
critical chemical potential would not happen anymore.
