We have carried out high-resolution near-infrared spectroscopic observations toward 16 Galactic supernova remnants (SNRs) showing strong H2 emission features. A dozen bright H2 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 H2 line ratios are well consistent with that of thermal excitation at T ~ 2000 K, indicating that the H2 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 H2 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 H2 emission lines for six SNRs are well consistent (±5 km/s) 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 H2 emission shows nonthermal line ratios and narrow line width (~4 km/s), and we discuss its origin.