We examine the spectral characteristics of normal OB stars with high-signal-to-noise ratio (> 120) H-band (1.6 mu m) spectra at a resolution of 2000. We find that several atomic lines vary smoothly with stellar temperature, as first shown by Blum et al. However, we find a previously unreported, significant variation in the strength of some of these lines with stellar luminosity. B supergiant stars show stronger He I and weaker Br 11 as compared with low-luminosity B dwarf stars of the same spectral class. It is for this reason that luminosity class must also be determined to obtain an accurate spectral type for a given star using H-band spectra. We suggest a method for estimating the spectral type and luminosity of an OB star over the wavelength range from 1.66 to 1.72 mu m using hydrogen Br 11 at 1.681 mu m, He I at 1.700 mu m, and He II at 1.693 mu m. The use of the near-infrared spectral range for classification has obvious advantages over optical classification when applied to heavily reddened stars, such as in star-forming regions or deeply embedded lines of sight within the plane of the Galaxy, such as the Galactic center. Furthermore, the H band is less likely to be contaminated by infrared excess emission, which is frequently seen around massive young stellar objects beyond 2 mu m.