A(3)B(8)O(21) hexagonal perovskite-like Ba3Ti4Nb4O21 ceramics were synthesized by a conventional solid-state reaction technique, which exhibit high dielectric constant at room temperature. A high-temperature dielectric relaxation was observed in frequency range from 40 Hz to 1 MHz above the Curie temperature. The real and imaginary parts of the impedance (Z' and Z") as functions of frequency indicate the presence of two relaxation processes at high temperatures, which are attributed to grain and grain boundary responses. The conductivities of both grain and grain boundary obey the Arrhenius law with activation energies of 1.04 eV and 1.27 eV, respectively. The dielectric relaxation processes are related to the oxygen vacancies inside the ceramic, indicating that the Q x f value of Ba3Nb4Ti4O21 might be improved via eliminating oxygen vacancies. (C) 2013 Elsevier B.V. All rights reserved.