The pure, 2 at.%, and 20 at.% Gd-doped HfO2 ceramics were prepared by the standard solid-state reaction technique. Dielectric properties of these ceramics were investigated in the temperature range 300-1050 K and frequency range 20-5 x 10(6) Hz. Our results revealed an intrinsic dielectric constant around 20 in the temperature below 450 K for all tested ceramics. Two oxygen-vacancy-related relaxations R1 and R2 were observed at temperatures higher than 450 K, which were identified to be a dipolar relaxation due to grain response and a Maxwell-Wagner relaxation due to grain-boundary response, respectively. The dielectric properties of the pure and slightly doped (2 at.%,) samples are dominated by the grain-boundary response, which results in a colossal dielectric behavior similar to that found in CaCu3Ti4O12. The doping level of 20 at.% leads to the structural transformation from monoclinic phase to cubic phase. The dielectric properties of the heavily doped HfO2 are dominated by the grain response without any colossal dielectric behavior.