The atomistic and electronic structures of PbTiO3 nanowires with characteristic edges consisting of (100) and (010) surfaces and the crucial role of axial tensile strain on ferroelectricity have been investigated by means of ab initio density-functional theory calculations. Ferroelectricity is enhanced at the edge of the PbO-terminated nanowire because the Pb-O covalent bond that predominates ferroelectric distortions is locally strengthened. On the other hand, a considerable suppression is found in the TiO2-terminated nanowire, caused by the charge transfer from the Pb-O site to the Ti-O site. Surprisingly, the smallest PbO-terminated nanowire with a cross section of only one-unit cell can possess ferroelectricity while ferroelectricity disappears in the TiO2-terminated nanowires with a cross section smaller than four-by-four cells (diameter of about 17 Å). However, ferroelectricity is recovered by axial tension, where smaller nanowires require larger critical strains.