  We investigate the dispersion relation of M\"obius domain-wall fermions in
free field theory at finite $L_s$. We find that there are $L_s-1$ extra poles
of M\"obius domain-wall fermions in addition to the pole which realizes the
physical mode in the continuum limit. The unphysical contribution of these
extra poles could be significant when we introduce heavy quarks. We show in
this report the fundamental properties of these unphysical poles and discuss
the optimal choice of M\"obius parameters to minimize their contribution to
four-dimensional physics.
