Doping of the SrTiO3 surface with non-metal atoms (X = C, N, F, Si, P, S, Cl, Se, Br and I) has been considered in a systematic study by performing periodic density functional theory calculations using the hybrid HSE06 functional, with the objective of improving its photocatalytic activity for water splitting under visible light. Our results found that the doping in the top layer of the SrTiO3(001) surface is energetically favored. An X (X = C, N and F) atom with a relatively small atomic radius tends to substitute the O atom in the TiO2-terminated surface, while the preferential occupation of the X (X = P, S, Cl, Se and Br) atom with larger atomic radius takes place at the O position in the SrO-terminated surface. X-doped surfaces (X = C, Si and P) show the presence of discrete midgap states, which are detrimental to photocatalysis. Due to the appearance of surface O 2p states, the band gap of the pure TiO2-terminated surface is calculated to be 2.56 eV, which is much narrower than that of bulk SrTiO3 (3.4 eV). Our results indicate that the band alignments of N-doped, Br-doped and I-doped SrTiO3(001) surfaces are well positioned for the feasibility of photo-oxidation and photo-reduction of water, which are promising for water splitting in the visible light region.