BiCr0.5Mn0.5O3, synthesized at high pressure and high temperature, has a monoclinic structure (space group C2/c) at room temperature with a = 9.4590(3) Å, b = 5.5531(2) Å, c = 9.6465(3) Å and β = 108.149(2)°. It undergoes a structural transition from the monoclinic to an orthorhombic (Pnma) symmetry around 650 K. Magnetic measurements show three distinct anomalies at 25, 50 and 97 K. AC susceptibility measurements confirm the occurrence of the magnetic anomalies, but suggest no spin frustration. Interestingly, this oxide shows a giant dielectric constant at room temperature. Two clear relaxation processes commencing around 200 K and 300 K are exhibited by this material. The first relaxation process is due to Maxwell-Wagner polarization at the grain boundary whereas the second relaxation may arise from hopping of electrons in the B-site. © 2010 The Royal Society of Chemistry.