The crystal structure and superconducting properties of monatomic bromine under high pressure have been studied by first-principles calculations. We have found the following phase transition sequence with increasing pressure: from body-centered orthorhombic (bco, phase II) to body-centered tetragonal structure (bct, phase III) at 126 GPa, then to face-centered cubic structure (fcc, phase IV) at 157 GPa, which is stable at least up to 300 GPa. The calculated superconducting critical temperature T(c) = 1.46 K at 100 GPa is consistent with the experimental value of 1.5 K. In addition, our results of T(c) decrease with increasing pressure in all the monatomic phases of bromine, similar to monatomic iodine. Further calculations show that the decrease of λ with pressure in phase IV is mainly attributed to the weakening of the 'soft' vibrational mode caused by pressure.