We report the results of our analysis of the H II region around ζ Oph based on far-ultraviolet (FUV) spectral imaging observations, together with data made in other wavelengths. We found that scattering by dust grains of the FUV photons, which originate mostly from ζ Oph, dominates the FUV emission in this region, while contributions from the two-photon effects and molecular hydrogen fluorescence are not negligible. Unlike the Hα image, which shows dark shadows of the molecular clouds on the extended diffuse background, the FUV continuum image is featureless with a smooth intensity that decreases outward from the center, which is attributed to multiple scattering of photons originating from a single star that smears out the shape of the scattering dust clouds. Molecular hydrogen fluorescence emission is enhanced at the boundary of the H II region, especially in LDN 204 at its closest region facing ζ Oph. The region has a high temperature of ~1000 K as well as high atomic and molecular hydrogen content with n H = ~101.8 cm-3 and N(H2) = ~1022 cm-2, respectively. Photoionization and dust-scattering simulations are conducted with the effects of molecular clouds included, and the results are compared with the corresponding Hα and FUV observations. The results suggest that the molecular clouds reside close to the H II region in front of ζ Oph and that they may partially overlap with the H II region.