  We study the effects of isovector-scalar meson $\delta$ on the equation of
state (EOS) of neutron star matter in strong magnetic fields. The EOS of
neutron-star matter and nucleon effective masses are calculated in the
framework of Lagrangian field theory, which is solved within the mean-field
approximation. From the numerical results one can find that the $\delta$-field
leads to a remarkable splitting of proton and neutron effective masses. The
strength of $\delta$-field decreases with the increasing of the magnetic field
and is little at ultrastrong field. The proton effective mass is highly
influenced by magnetic fields, while the effect of magnetic fields on the
neutron effective mass is negligible. The EOS turns out to be stiffer at $B <
10^{15}$G but becomes softer at stronger magnetic field after including the
$\delta$-field. The AMM terms can affect the system merely at ultrastrong
magnetic field($B > 10^{19}$G). In the range of $10^{15}$ G -- $10^{18}$ G the
properties of neutron-star matter are found to be similar with those without
magnetic fields.
