Pb2MnTeO6, a new double perovskite, was synthesized. Its crystal structure was determined by synchrotron X-ray and powder neutron diffraction. Pb2MnTeO6 is monoclinic (I2/m) at room temperature with a regular arrangement of all the cations in their polyhedra. However, when the temperature is lowered to similar to 120 K it undergoes a phase transition from I2/m to C2/c structure. This transition is accompanied by a displacement of the Pb atoms from the center of their polyhedra due to the 6s2 lone-pair electrons, together with a surprising off-centering of Mn2+ (d5) magnetic cations. This strong first-order phase transition is also evidenced by specific heat, dielectric, Raman, and infrared spectroscopy measurements. The magnetic characterizations indicate an anti-ferromagnetic (AFM) order below TN approximate to 20 K; analysis of powder neutron diffraction data confirms the magnetic structure with propagation vector k = (0 1 0) and collinear AFM spins. The observed jump in dielectric permittivity near similar to 150 K implies possible anti-ferroelectric behavior; however, the absence of switching suggests that Pb2MnTeO6 can only be antipolar. First-principle calculations confirmed that the crystal and magnetic structures determined are locally stable and that anti-ferroelectric switching is unlikely to be observed in Pb2MnTeO6.