  The origin of dust in galaxy halos or in the circum-galactic medium (CGM) is
still a mystery. We investigate if the radiation pressure in high-redshift
($z\sim 10$) galaxies can efficiently transport dust to halos. To clarify the
first dust enrichment of galaxy halos in the early Universe, we solve the
motion of a dust grain considering radiation pressure, gas drag, and gravity in
the vertical direction of the galactic disc. Radiation pressure is estimated in
a consistent manner with the stellar spectra and dust extinction. As a
consequence, we find that dust grains with radii $a\sim 0.1~\mu$m successfully
escape from the galactic disc if the ongoing star formation episode converts
more than 15 per cent of the baryon content into stars and lasts $\gtrsim 30$
Myr, while larger and smaller grains are trapped in the disc because of gravity
and gas drag, respectively. We also show that grain charge significantly
enhances gas drag at a few--10 scale heights of the galactic disc, where the
grain velocities are suppressed to $\sim 1$ km s$^{-1}$. There is an optimum
dust-to-gas ratio ($\sim 10^{-3}$) in the galactic disc and an optimum virial
mass $\sim 10^{10}$--$10^{11}$ M$_{\odot}$ for the transport of $a\sim
0.1~\mu$m grains to the halo. We conclude that early dust enrichment of galaxy
halos at $z\gtrsim 10$ is important for the origin of dust in the CGM.
