The gradual diffusion of an antiferroelectric phase transition of NaNbO3 single crystals, while doped with Gd, was investigated. A Landau-type theory that includes the coupling of and order parameter with local quenched fields was used to describe the diffuseness of the phase transition. The x-ray diffraction analysis was used to study the single crystals. The expressions obtained by the theory described both the Curie-Weiss behavior of dielectric permitivity above and below Curie-Weiss temperature and temperature dependence of inverse dielectric permittivity in the intermediate region.