Diamond anvil cells combined with Raman spectroscopy and synchrotron X-ray diffraction were used to analyze the compression behavior of sulfamide, a hydrogen-bonded crystal. The marked changes in the Raman spectra at approximately 5 GPa strongly suggest a structural phase transition associated with the rearrangement of hydrogen bonds. Results from angle-dispersive X-ray diffraction confirmed this pressure-induced phase transition, and the high-pressure phase was indexed and refined to a low-symmetry monoclinic structure with space group I2/m. Further phase transitions were not detected up to the maximum pressure of 10 GPa. The observed transition was completely reversible when the pressure was released to ambient conditions. The results from ab initio calculations reveal that the phase transition was mainly caused by changes in the hydrogen-bond networks in sulfamide.