We explore the relationships between the 3.3 μm polycyclic aromatic hydrocarbon (PAH) feature and active galactic nucleus (AGN) properties of a sample of 54 hard X-ray selected bright AGNs, including both Seyfert 1 and Seyfert 2 type objects, using 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 and all of them have measured X-ray spectra at E ≲ 10 keV. These X-ray spectra provide measurements of the neutral hydrogen column density (N H) towards the AGNs. We use the 3.3 μm PAH luminosity (L 3.3μm) as a proxy for star formation activity and hard X-ray luminosity (L 14-195keV) as an indicator of the AGN activity. We searched for possible difference of star-formation activity between type 1 (un-absorbed) and type 2 (absorbed) AGNs. Our regression analysis of log L 14-195keV versus log L 3.3μm shows a positive correlation and the slope seems steeper for type 1/unobscured AGNs than that of type 2/obscured AGNs. The same trend has been found for the log (L 14-195keV/M BH) versus log (L 3.3μm/MBH) correlation. Our analysis show that the circum-nuclear star-formation is more enhanced in type 2/absorbed AGNs than type 1/un-absorbed AGNs for low X-ray luminosity/low Eddington ratio AGNs.