As promising photocatalyst driven by visible-light, BiOI has attracted more and more attention in the past years. However, the surface structure and properties of BiOl that is the most important place for the photocatalytic have not been investigated in details. To this end, density functional theory was performed to calculate the structural and electronic properties of four low-index stoichiometric surfaces of BiOI. It is found that the relaxation of the low-index BiOI surfaces are relatively small, especially the (001) surface. Thus, the surface energies of BiOl are very relatively small. Moreover, there are a few surface states below the bottom of conduction band in the first layer except the (001) surface, which maybe capture the photo-excited carriers. In all of the most stable terminated planes, all the dangling bonds are cleaved from the broken Bi-O bonds. In the case of (001) surface, the dangling bond density of Bi atoms for the (001) surface is zero per square nano. Therefore, the (001) surface is thermodynamically lowest energy surface of BiOl, and it is the predominant surface (51.4%). As a final remark, the dangling bonds density of bismuth atoms determines not only the surface energy, but also the surface relaxation. Finally, the equilibrium morphology of BiOI was also proposed and provided, which is determined through the Wulff construction. These results will help us to better understand the underlying photocatalytic mechanism that is related to BiOI surfaces, and provide theoretical support for some experimental studies about BiOI-based photocatalyst in future. (C) 2017 Elsevier B.V. All rights reserved.