We utilize AKARI's slitless spectroscopic capability to detect the 3.3 μm polycyclic aromatic hydrocarbons (PAHs) emission and measure star formation (SF) activity for various AKARI programs. First, we obtain 2∼5μm spectra of 20 flux-limited galaxies with mixed SED classes in order to calibrate the 3.3 μm PAH luminosity (LPAH 3.3) as a star formation rate (SFR) indicator. We find that LPAH3.3 correlates with LIR as well as with the 6.2 μm PAH luminosity ( LPAH 6.2). The correlations does not depend on SED classes. We find that ULIRGs deviate from the correlation between PAH luminosities and LIR, while they do not for the correlation between PAH luminosities. We suggest possible effects to cause this deviation. On the other hand, how AGN activity is linked to SB activity is one of the most intriguing questions. While it is suggested that AGN luminosity of quasars correlates with starburst (SB) luminosity, it is still unclear how AGN activity is connected to SF activity based on host galaxy properties. We are measuring SFRs for the LQSONG sample consisting of reverberation mapped AGNs and PG-QSOs. This is an extension of the ASCSG program by which we investigated the connection between SB and AGN activities for Seyferts type 1s at z ~ 0.36. While we found no strong correlation between LPAH3.3 and AGN luminosity for these Seyferts 1s, LPAH3.3 measured from the central part of galaxies correlates with AGN luminosity, implying that SB and AGN activities are directly connected in the nuclear region.