Ab initio calculations are performed to probe the hydrogen bonding, structural, and superconducting behaviors of HBr and HCl under high pressure. The calculated results show that the hydrogen bond symmetrization (Cmc2(1)-->Cmcm transition) of HBr and HCl occurs at 25 and 40 GPa, respectively, which can be attributed to the symmetry stretching A(1) mode softening. After hydrogen bond symmetrization, a pressure-induced soft transverse acoustic phonon mode of Cmcm phase is identified and a unique metallic phase with monoclinic structure of P2(1)/m (4 molecules/cell) for both compounds is revealed by ab initio phonon calculations. This phase preserves the symmetric hydrogen bond and is stable in the pressure range from 134 to 196 GPa for HBr and above 233 GPa for HCl, while HBr is predicted to decompose into Br(2)+H(2) above 196 GPa. Perturbative linear-response calculations predict that the phase P2(1)/m is a superconductor with T(c) of 27-34 K for HBr at 160 GPa and 9-14 K for HCl at 280 GPa.