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 ∼ 2000 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 (±5 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 (∼ 4 km s −1), and we discuss its origin.