For high luminosity in electron-positron linear colliders, it is essential to generate low vertical emittance beams. We report on the smallest vertical emittance achieved in single-bunch-mode operation of the Accelerator Test Facility, which satisfies the requirement of the x-band linear collider. The emittances were measured with a laser-wire beam-profile monitor installed in the damping ring. The bunch length and the momentum spread of the beam were also recorded under the same conditions. The smallest vertical rms emittance measured at low intensity is 4 pm at a beam energy of 1.3 GeV, which corresponds to the normalized emittance of 1.0x1.0(-8) m. It increases by a factor of 1.5 for a bunch intensity of 10(10) electrons. The measured data agreed to the calculation of intrabeam scattering within much better than a factor of 2.