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 $Tsim2000$ 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.
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