  We have carried out high-resolution near-infrared spectroscopic observations
toward 16 Galactic supernova remnants (SNRs) showing strong H$_{2}$ emission
features. A dozen bright H$_{2}$ emission lines are clearly detected for
individual SNRs, and we have measured their central velocities, line widths,
and fluxes. For all SNRs except one (G9.9$-$0.8), the H$_{2}$ line ratios are
well consistent with that of thermal excitation at $T\sim2000$ K, indicating
that the H$_{2}$ emission lines are most likely from shock-excited gas and
therefore that they are physically associated with the remnants. The kinematic
distances to the 15 SNRs are derived from the central velocities of the H$_{2}$
lines using a Galactic rotation model. We derive for the first time the
kinematic distances to four SNRs: G13.5$+$0.2, G16.0$-$0.5, G32.1$-$0.9, and
G33.2$-$0.6. Among the remaining 11 SNRs, the central velocities of the H$_{2}$
emission lines for six SNRs are well consistent ($\pm5$ km s$^{-1}$) with those
obtained in previous radio observations, while for the other five SNRs
(G18.1$-$0.1, G18.9$-$1.1, Kes 69, 3C 396, W49B) they are significantly
different. We discuss the velocity discrepancies in these five SNRs. In
G9.9$-$0.8, the H$_{2}$ emission shows nonthermal line ratios and narrow line
width ($\sim 4$ km s$^{-1}$), and we discuss its origin.
