NaxBi(2-x)/3Cu3Ti4O12 (0.00 <= x <= 0.50) ceramics were prepared by conventional solid-state reaction method. The influence of Na substitution for Bi3+ on phase structure, microstructure, and dielectric properties was studied. It was found that the low-frequency dielectric constant increased with the increase of Na+ content. NaxBi(2-x)/3Cu3Ti4O12 ceramics with x = 0.35 showed the lowest dielectric loss (0.015) at 1 kHz with a relatively high dielectric permittivity (similar to 7600) among the prepared ceramics. The complex impedance spectroscopy at room temperature suggested that all the NaxBi(2-x)/3Cu3Ti4O12 ceramics were electrically heterogeneous. The calculated grain boundaries resistance and grain resistance decreased with increasing Na+ content. In view of the analyses of electric modulus, it could be concluded that the giant low-frequency dielectric constant observed in NaxBi(2-x)/3Cu3Ti4O12 ceramics was attributed to Maxwell-Wagner polarization at the grain boundaries. Furthermore, three dielectric relaxations existed in the temperature dependence of dielectric constant of NaxBi(2-x)/3Cu3Ti4O12 ceramics were possibly related to oxygen vacancies. (C) 2015 Elsevier Ltd. All rights reserved.