Luminous infrared galaxies (LIRGs) are enshrouded by a large amount of dust, produced by their active star formation, and it is difficult to measure their activity in the optical wavelength. We have carried out Pa$alpha$ narrow-band imaging observations of 38 nearby star-forming galaxies including 33 LIRGs listed in $IRAS$ RBGS catalog with the Atacama Near InfraRed camera (ANIR) on the University of Tokyo Atacama Observatory (TAO) 1.0 m telescope (miniTAO). Star formation rates (SFRs) estimated from the Pa$alpha$ fluxes, corrected for dust extinction using the Balmer Decrement Method (typically $A_V$ $sim$ 4.3 mag), show a good correlation with those from the bolometric infrared luminosity of $IRAS$ data within a scatter of 0.27 dex. This suggests that the correction of dust extinction for Pa$alpha$ flux is sufficient in our sample. We measure the physical sizes and the surface density of infrared luminosities ($Sigma_{L(mathrm{IR})}$) and $SFR$ ($Sigma_{SFR}$) of star-forming region for individual galaxies, and find that most of the galaxies follow a sequence of local ultra luminous or luminous infrared galaxies (U/LIRGs) on the $L(mathrm{IR})$-$Sigma_{L(mathrm{IR})}$ and $SFR$-$Sigma_{SFR}$ plane. We confirm that a transition of the sequence from normal galaxies to U/LIRGs is seen at $L(mathrm{IR})=8times10^{10}$ $L_{odot}$. Also, we find that there is a large scatter in physical size, different from those of normal galaxies or ULIRGs. Considering the fact that most of U/LIRGs are merging or interacting galaxies, this scatter may be caused by strong external factors or differences of their merging stage.
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