We present medium-resolution spectra (R~2000-4000) at 0.4-1.0{mu}m and 0.7-2.5{mu}m of 16 active galactic nuclei (AGNs) selected with red color in the near-infrared (NIR) of J-K>2.0mag at z~0.3. We fit the H{beta}, H{alpha}, P{beta}, and P{alpha} lines from these spectra to obtain their luminosities and line widths. We derive the E(B-V) color excess values of the NIR-red AGNs using two methods, one based on the line-luminosity ratios and another based on the continuum slopes. The two E(B-V) values agree with each other at rms dispersion ~0.249. About half of the NIR-red AGNs have g'-K<5 magnitude, and we find that these NIR-red, but blue in optical-NIR AGNs, have E(B-V)~0, suggesting that a significant fraction of the NIR color-selected red AGNs are unobscured or only mildly obscured. After correcting for the dust extinction, we estimate the black hole (BH) masses and the bolometric luminosities of the NIR-red AGNs using the Paschen lines to calculate their Eddington ratios ({lambda}Edd). The median Eddington ratios of nine NIR-red AGNs (log({lambda}_Edd_~-0.654+/-0.176) are only mildly higher than those of unobscured type 1 AGNs (log({lambda}_Edd_~-0.961+/-0.008). Moreover, we find that the MBH-{sigma}* relation for three NIR-red AGNs is consistent with that of unobscured type 1 AGNs at similar redshift. These results suggest that the NIR-red color selection alone is not effective at picking up dusty, intermediate-stage AGNs.