We present the 9 and 18 micron 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 9 micron and 255 galaxies at 18 micron 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 18 micron luminosity.