A giant low-frequency dielectric constant ( epsilon 0 approximately 10(5)) near room temperature was observed in Li,Ti co-doped NiO ceramics. Unlike currently best-known high epsilon 0 ferroelectric-related materials, the doped oxide is a nonperovskite, lead-free, and nonferroelectric material. It is suggested that the giant dielectric constant response of the doped NiO could be enhanced by a grain boundary-layer mechanism as found in boundary-layer capacitors. In addition, there is about a one-hundred-fold drop in the dielectric constant at low temperature. This anomaly is attributed to a thermally excited relaxation process rather than a thermally driven phase transition, as for that yielding ferroelectrics.