The crystal structures of boron hydrides in a pressure range of 50–400 GPa were studied using the genetic algorithm (GA) method combined with first-principles density functional theory calculations. BH4 and BH5 are predicted to be thermodynamically unstable. Two new BH2 structures with Cmcm and C2/c space group symmetries, respectively, were predicted, in which the B atoms tend to form two-dimensional sheets. The calculated band structures showed that in the pressure range of 50–150 GPa, the Cmcm-BH2 phase has very small gaps, while the C2/c-BH2 phase at 200–400 GPa is metallic. The superconductivity of the C2/c-BH2 structure was also investigated, and electron–phonon coupling calculations revealed that the estimated Tc values of C2/c-BH2 are about 28.18–37.31 K at 250 GPa.