Under GGA, the structural, electronic properties and stabilities of four different (1 x 1) terminations of cubic PbTiO3 (1 1 1) surface, the directly cleaved (1 1 1)-Ti and (1 1 1)-PbO3 terminations and the constructed (1 1 1)-TiO and (1 1 1)-PbO2 ones, have been systematically studied by using projector-augmented wave method implemented in VASP. For (1 1 1)-Ti and (1 1 1)-PbO3 terminations, Ti-O bonds between the outermost two layers are enhanced after relaxation, while those between the second and the third layers are weakened. In addition, a contraction of O-O distance in surface PbO3 layer is also found for (1 1 1)- PbO3 termination. Moreover, electronic structures of both (1 1 1)-Ti and (1 1 1)-PbO2 terminations are significantly influenced by structure relaxations, and the effects of the surface on the DOS are dominantly on the Ti layers, especially the CB. For a constructed (1 1 1)-TiO termination, the relaxation results show both Ti-O bonds between the outermost two layers and those between the second PbO3 layer and the third Ti layers are enhanced. For a constructed (1 1 1)-PbO2 termination, Ti-O bonds between the outermost two layers are also enhanced as in the (1 1 1)-TiO termination, however, inequivalent Ti-O bonds between the second layer Ti atom and the third layer O atoms are found, with two bonds expanding and the other one contracting. Results of electronic structure calculations show these two constructed terminations are all insulating and changes of DOS originate dominantly from modifications of surface compositions. Furthermore, it is found that for all four different (1 1 1) terminations, the movements of the cation and/or anion on the outermost layer along the surface normal direction after relaxation all result in a reduction of the space electric field. In O and Pb external environments, it is predicted that (1 1 1)-PbO2 termination is the most stable one in O- and Pb-rich environments, however, the (1 1 1)-Ti termination is stable one in O-and Pb-poor conditions. The (1 1 1)-TiO termination also shows a stability domain in moderate O and Pb environments. (C) 2009 Elsevier B.V. All rights reserved.