Using extensive mid-IR datasets from AKARI, i.e. 9-band photometry covering the wavelength range from $2{mu}m$ to $24{mu}m$ and the unbiased spectroscopic survey for sources with $S_{ u}$($9{mu}m$)>0.3 mJy, we study starburst galaxies specifically at the redshift of z ~ 0.5, whose mid-IR spectra are clearly dominated by the PAH emission features. PAH-selected galaxies, selected with extremely red mid-IR colour due to PAHs, have high rest-frame PAH-to-stellar luminosity ratios, comparable to those in the most active regions in nearby starburst galaxies. Thus, they seem to have active starburst regions spreading over the whole body. Furthermore, some of PAH-selected galaxies are found to have peculiar rest-frame 11-to-$8{mu}m$ flux ratios, which is systematically smaller than nearby starburst/AGN spectral templates. This may indicate a systematic difference in the physical condition of ISM between nearby and distant starburst galaxies.