  We investigate the two dimensional lattice Gross--Neveu model in large flavor
number limit using the domain-wall fermion formulation, as a toy model of
lattice QCD. We study nonperturbative behaviorn of the restoration of chiral
symmetry of the domain-wall fermions as the extent of the extra dimension
$(N_s)$ is increased to infinity. We find the the parity broken phase (Aoki
phase) for finite $N_s$, and study the phase diagram, which is related to the
mechanism of the chiral restoration in $N_s\to\infty$ limit. The continuum
limit is taken and $O(a)$ scaling violation of observables vanishes in
$N_s\to\infty$ limit. We also examine the systematic dependencies of
observables to the parameters.
