The dielectric properties and nonlinear current-voltage characteristics of Na1/2Sm1/2Cu3Ti4O12 ceramics prepared by a conventional solid state reaction method were investigated. Na1/2Sm1/2Cu3Ti4O12 ceramics exhibited a high dielectric permittivity of 7.0-8.4 x 10(3) and low loss tangent (tan delta similar to 0.030-0.041). Non-Ohmic properties with a high breakdown voltage of similar to 2208 V cm(-1) and large nonlinear coefficient of 15.6 were observed in Na1/2Sm1/2Cu3Ti4O12 ceramics. Using complex impedance analysis, Na1/2Sm1/2Cu3Ti4O12 ceramics were shown to be electrically heterogeneous consisting of semiconducting grains and insulating grain boundaries. Giant dielectric properties were described based on the electrically heterogeneous microstructure. X-ray photoelectron spectroscopy analysis suggested that the semiconductive nature of grains may be related to the presence of Cu+ and Ti3+. The formation of an electrostatic potential barrier at the grain boundaries of Na1/2Sm1/2Cu3Ti4O12 ceramics was suggested to be caused by the Schottky effect. Interestingly, high electrostatic potential barriers at grain boundaries in Na1/2Sm1/2Cu3Ti4O12 ceramics were calculated and found to be 0.925-0.964 eV. (c) 2013 Elsevier Ltd. All rights reserved.