We have performed first-principles calculations to investigate the behavior of the hydrogen bond in δ-AlOOH under pressure. The highest OH-stretching A1 and B2 mode frequencies decrease under pressure leading to hydrogen bond symmetrization. After hydrogen bond symmetrization, the corresponding frequencies gradually increase. This softening and subsequent hardening of the OH bonds is a good spectroscopic indicator of hydrogen bond symmetrization and is observed in our GGA static calculations at ~30 GPa without considering tunneling effects. We have also carried out calculations of Raman peak intensities in several supercells with various hydrogen orderings to investigate the potential effect of H-disorder on the Raman spectrum of δ-AlOOH. Our results suggest that the four broad Raman bands observed experimentally in the range of OH-stretching mode frequencies could originate in H-disorder in this phase.