We present the 9 and 18um luminosity functions (LFs) of galaxies at 0.006<=z<=0.8 (with an average redshift of ~0.04) using the AKARI mid-infrared all-sky survey catalog. We selected 243 galaxies at 9um and 255 galaxies at 18um from the Sloan Digital Sky Survey (SDSS) spectroscopy region. These galaxies were then classified by their optical emission lines, such as the line width of H{alpha} or by their emission line ratios of [OIII]/H{beta} and [NII]/H{alpha} into five types: Type 1 active galactic nuclei (AGN) (Type 1); Type 2 AGN (Type 2); low-ionization narrow emission line galaxies (LINER); galaxies with both star formation and narrow-line AGN activity (composite galaxies); and star-forming galaxies (SF). We found that (i) the number density ratio of Type 2 to Type 1 AGNs is 1.73+/-0.36, which is larger than a result obtained from the optical LF and (ii) this ratio decreases with increasing 18um luminosity.