The compound BiCr0.5Mn0.5O3, synthesized at high pressure and high temperature, shows a giant dielectric constant over a wide range of temperatures. Two relaxation processes are observed commencing around 200 K and 300 K. The low-temperature relaxation process is attributed to Maxwell–Wagner polarization at the grain boundary, whereas the second relaxation is attributed to the electrode polarization effect. Impedance spectroscopy reveals that the oxide is electrically inhomogeneous and dominant contribution arises from semiconducting grains and insulating grain boundary below room temperature. Above room temperature, the electrode polarization effect also contributes to the observed giant dielectric constant.