The structure, electronic and magnetic properties have been investigated by the rst-principles calculations for paramagnetic, ferromagnetic and antiferromagnetic Cu 3 TeO 6 under pressure from 0 to 100 GPa. The calculated lattice parameters at 0 GPa are in excellent agreement with the available calculated and experimental values. With increasing pressure, the lattice parameters and volume decrease, but Cu 3 TeO 6 keep a stable cubic structure. The electronic calculations show that paramagnetic and ferromagnetic Cu 3 TeO 6 are metallic, and antiferromagnetic Cu 3 TeO 6 has the non-metallic nature with a direct band gap which decreases with the increasing pressure. Under the pressure, their non-locality of density of states enhances and the electrons becomes more active. Moreover, for antiferromagnetic Cu 3 TeO 6, the spin moments of Cu atoms are affected obviously by pressures, and Te atoms show nonmagnetic performance. The total magnetic moment which is mainly contributed by Cu, reaches the maximum at 20 GPa, and decreases with the increasing pressure. The knowledge of these properties will provide reference and guidance for the subsequent study of Cu 3 TeO 6 .