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 ($zsim 10$) 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 $asim 0.1~mu$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 $asim 0.1~mu$m grains to the halo. We conclude that early dust enrichment of galaxy halos at $zgtrsim 10$ is important for the origin of dust in the CGM.
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