The localization of a two-level atom placed in an optical cavity containing a standing wave is investigated, and the single atomic-position can be well-localized by the way of quadrature-field measurement. According to the Rayleigh limit when two two-level atoms are put in the cavity, it is difficult to distinguish between the two atoms if they are very close to each other. Also, the two atoms can be still well-distinguished by quadrature-field measurement. However, if the cavity damping is taken into account, the two-atom relative position localization will be damaged. The larger damping rate of the cavity become, the worse the two-atom relative position localization will be.