  We construct a novel $ N_f = 2 $ pseudofermion action for Monte-Carlo
simulation of lattice gauge theory with domain-wall fermions (DWF), of which
the effective four-dimensional lattice Dirac operator is equal to the
overlap-Dirac operator with the argument of the sign function equal to $ H = c
\gamma_5 D_w (1 + d D_w)^{-1} $, where $ c $ and $ d $ are parameters, and
$D_w$ is the standard Wilson-Dirac operator plus a negative parameter $-m_0 \;
(0 < m_0 < 2)$. This new action is particularly useful for the challenging
simulations of lattice gauge theories with large $N_f = 2n $ DWF, on the large
lattices, and in the strong-coupling regime.
