We investigate the relation between star formation activity and PAH $3.3{mu}m$ emission. Our targets are mid-infrared-excess galaxies selected from the AKARI all-sky survey point source catalog. We performed AKARI near-infrared spectroscopy for them. As a result, we obtained $2.5-5{mu}m$spectra of 79 galaxies, and selected 35 star-forming galaxies out of them. Comparing the PAH $3.3{mu}m$ luminosities with the infrared luminosities, we find a linear correlation between them. However, by adding the results from literatures for luminous infrared galaxies and ultra-luminous infrared galaxies that are more luminous than our sample, the ratio of the PAH to the infrared luminosity is found to decrease towards the luminous end.