We present results of the 2.5-5 {mu}m spectroscopy of a sample of hard X-ray selected active galactic nuclei (AGNs) using the grism mode of the InfraRed Camera (IRC) on board the infrared astronomical satellite AKARI. The sample is selected from the 9-month Swift/BAT survey in the 14-195 keV band, which provides a fair sample of AGNs including highly absorbed ones. The 2.5-5 {mu}m spectroscopy provide a strong diagnostic tool for the circumnuclear environment of AGNs through the continuum shapes and emission/absorption features such as the 3.3 {mu}m polycyclic aromatic hydrocarbon (PAH) emission and the broad 3.1 {mu}m H2O ice, 3.4 {mu}m bare carbonaceous dust, 4.26 {mu}m CO2 and 4.67 {mu}m CO absorptions. As our first step, we use the 3.3 {mu}m PAH emission as a proxy for the star-formation activity and searched for possible difference of star-formation activity between type 1 (unabsorbed) and type 2 (absorbed) AGNs. We found no significant dependence of the 3.3 {mu}m PAH line luminosity, normalized by the black hole mass, on optical AGNs types or the X-ray measured column densities.