The stabilities and electronic/band structures of single-layer bismuth oxyhalides have been investigated by employing first-principles calculations. The results indicate that the single-layer bismuth oxyhalide materials, except for BiOF, have robust energetic and dynamical stabilities because of their low formation energies and the absence of imaginary frequencies within the entire Brillouin zone. Furthermore, calculations of the electronic structures and optical absorptions indicate that single-layer BiOI possesses a favorable band gap, suitable band edge positions, different orbital characteristics and different effective masses at the valence band maximum (VBM) and conduction band minimum (CBM), thus presenting excellent photocatalytic activity for water splitting. Moreover, the resulting compressive strains can shift the band edge positions of the single-layer materials to more suitable places to enhance their photocatalytic activities.