  We present a slowly rotating black hole with phantom global monopole by
solving Einstein's field equation and find that presence of global monopole
changes the structure of black hole. The metric coefficient $g_{t\phi}$
contains hypergeometric function of the polar coordinate $r$, which is more
complex than that in the usual slowly rotating black hole. The energy scale of
symmetry breaking $\eta$ affects the black hole horizon and a deficit solid
angle. Especially, the solid angle is surplus rather than deficit for a black
hole with the phantom global monopole. We also study the correction originating
from the global monopole to the angular velocity of the horizon $\Omega_H$, the
Kepler's third law, the innermost stable circular orbit and the radiative
efficiency $\epsilon$ in the thin accretion disk model. Our results also show
that for the phantom black hole the radiative efficiency $\epsilon$ is positive
only for the case $\eta\leq \eta_c$. The threshold value $\eta_c$ increases
with the rotation parameter $a$.
