  We present medium-resolution spectra ($R \sim 2000$--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 $J - K > 2.0$ mag at $z
\sim 0.3$. 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 $\sim$ 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 $E(B-V) \sim 0$, 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 ($\lambda_{\rm
Edd}$). The median Eddington ratios of nine NIR-red AGNs ($\log (\lambda_{\rm
Edd}) \simeq -0.654 \pm 0.176$) are only mildly higher than those of unobscured
type 1 AGNs ($\log (\lambda_{\rm Edd}) \simeq -0.961 \pm 0.008$). Moreover, we
find that the $M_{\rm BH}$--$\sigma_{\ast}$ 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.
