  Rapid localization of gravitational-wave events is important for the success
of the multi-messenger observations. The forthcoming improvements and
constructions of gravitational-wave detectors will enable detecting and
localizing compact-binary coalescence events even before mergers, which is
called early warning. The performance of early warning can be improved by
considering modulation of gravitational wave signal amplitude due to the Earth
rotation and the precession of a binary orbital plane caused by the misaligned
spins of compact objects. In this paper, for the first time we estimate
localization precision in the early warning quantitatively, taking into account
an orbital precession. We find that a neutron star-black hole binary at $z=0.1$
can typically be localized to $100\,\mathrm{deg}^2$ and $10\,\mathrm{deg^2}$ at
the time of $12$ -- $15 \,\mathrm{minutes}$ and $50$ -- $300\,\mathrm{seconds}$
before merger, respectively, which cannot be achieved without the precession
effect.
