The complex perovskite Pb(2)CoTeO(6) (PCTO) has been prepared as polycrystalline powders by a solid state reaction route, and the crystal structure and magnetic properties have been investigated using a combination of X-ray and neutron powder diffraction, electron microscopy, dielectric, calorimetric and magnetic measurements. It was shown that at room temperature this compound adopts a trigonal perovskite structure, space group R3 (a = 5.6782(1) Å, c = 13.8552(3) Å). The compound undergoes a number of temperature-induced phase transitions and adopts four different structures in the temperature range 5-500 K: monoclinic in P2(1)/n (5 < T < 125 K, tilt system (a(+)b(-)b(-))), monoclinic in I2/m (125 < T < 210 K, tilt system (a(0)b(-)b(-))), rhombohedral in R3 (210 < T < 370 K, tilt system (a(-)a(-)a(-))), and finally cubic in Fm3m (above 370 K without any tilting). These structural phase transitions are coupled to changes in the dielectric constant and the heat capacity around 210 and 370 K. A long-range antiferromagnetically ordered state has been identified from neutron powder diffraction and magnetic studies at different temperatures. Magnetic diffraction peaks were registered below the transition at about 16 K and a possible model for the magnetic structure is proposed. Possible coexistence of long-range ordering of the electrical dipoles and the magnetic moments at low temperatures making PCTO a potential multiferroic candidate is discussed.