Dy 2/3 Cu 3 Ti 4 O 12 ceramics were successfully synthesized by solid-state reaction process, and the crystal structure, microstructure and dielectric properties were systematically investigated. It has been found that Dy 2/3 Cu 3 Ti 4 O 12 ceramics exhibit giant dielectric constants (e 0 * 10 4 at 1 kHz and room temperature) and have two thermal-activated dielectric relaxations at low and high temperatures, which are quite similar to those reported in CaCu 3 Ti 4 O 12 ceramics. The low-temperature dielectric relaxation with the activation energy of 0.092 eV is supposed to be the intrinsic response originated from the defect structures of oxygen vacancy and aliovalences of Ti and Cu ions, which might make the grains semiconductive. Moreover, the heterogeneous structures especially the grain boundaries should be responsible for the high-temperature dielectric relaxation with the activation energy of 0.585 eV. The semiconducting grains and insulating grain boundaries thus play the key role as extrinsic origin for the giant dielectric response in Dy 2/3 Cu 3 Ti 4 O 12 ceramics according to the internal barrier layer capacitor (IBLC) mechanism.