  An analytical model is developed for the screening of the external magnetic
field of a rotating, axisymmetric neutron star due to the accretion of plasma
from a disk. The decrease of the field occurs due to the electric current in
the infalling plasma. The deposition of this current carrying plasma on the
star's surface creates an induced magnetic moment with a sign opposite to that
of the original magnetic dipole. The field decreases independent of whether the
star spins-up or spins-down. The time-scale for an appreciable decrease (factor
of $>100$) of the field is found to be $\sim 1.6 \times 10^7$ yr, for a mass
accretion rate $\dot{M}=10^{-9} M_\odot/$yr and an initial magnetic moment
$\mu_i = 10^{30}{\rm G cm}^3$ which corresponds to a surface field of $10^{12}
$G if the star's radius is $10^6$ cm. The time-scale varies approximately as
$\mu_i^{3.8}/\dot{M}^{1.9}$. The decrease of the magnetic field does not have a
simple relation to the accreted mass. Once the accretion stops the field leaks
out on an Ohmic diffusion time scale which is estimated to be $ > 10^9$ yr.
