The adsorption of atomic hydrogen on hexagonal boron nitride (h-BN) is studied using two element-specific spectroscopies, i.e., near-edge x-ray absorption fine structure (NEXAFS) spectroscopy and x-ray photoelectron spectroscopy (XPS). B K-edge NEXAFS spectra show a clear change in the energy region of the π* band before and after reaction with atomic deuterium. On the other hand, N K-edge NEXAFS spectra show only a little change. B 1s XPS spectra show a distinct component at the low binding energy side of a main component, while N 1s XPS spectra show peak broadening at the high binding energy side. These experimental results are analyzed by the discrete variational Xα method with a core-hole effect and are explained by a model in which hydrogen atoms are preferentially adsorbed on the B sites of h-BN. Based on the experimental and theoretical results, we propose a site-selective property of BN material on adsorption of atomic hydrogen.