We have performed dispersion-corrected first-principles calculations of crystalline α-D-glucose anhydride and the monohydrate and measured its terahertz spectrum at 4 and 300K, to reveal the terahertz vibrations and the spectral change with hydration. Dispersion-corrected first-principles calculations well reproduced the 4-K spectrum, in both the frequency values and the relative tendency of intensities. The difference from the weak-hydrogen-bonding system is that most intermolecular modes were clearly detected even at 300K. The stretching vibration of moderate hydrogen bond was mixed with one of intermolecular rotation modes. With dehydration of the monohydrate, two intermolecular translational modes appear in the THz region.