  In this paper, we present an expanding disc model to derive polarization
properties of the Crab nebula. The distribution function of the plasma and the
energy density of the magnetic field are prescribed as function of the distance
from the pulsar by using the model by Kennel and Coroniti (1984) with $\sigma =
0.003$, where $\sigma$ is the ratio of Poynting flux to the kinetic energy flux
in the bulk motion just before the termination shock. Unlike previous models,
we introduce disordered magnetic field, which is parameterized by the
fractional energy density of the disordered component. Flow dynamics is not
solved. The mean field is toroidal. Averaged polarization degree over the disc
is obtained as a function of inclination angle and fractional energy density of
the disordered magnetic field. It is found for the Crab that the disordered
component has about 60 percent of the magnetic field energy. This value is also
supported by the facts that the disc appears not `lip-shape' but as `rings' in
the intensity map as was observed, and that the highest polarization degree of
$\sim 40$ percent is reproduced for rings, being consistent with the
observation. We suggest that because the disordered field contributes rather
pressure than tension, the pinch force may be over-estimated in previous
relativistic magnetohydrodynamic simulations. Disruption of the toroidal
magnetic field with alternating direction, which is proposed by Lyubarski
(2003), may actually takes place. The relativistic flow speed, which is
indicated by the front-back contrast, can be detected in asymmetry in
distributions of the position angle and depolarization.
