The synthesis, crystal structure, and dielectric properties of the novel double perovskite Pb2TmSbO6 are described. The room-temperature crystal structure was determined by ab initio procedures from neutron powder diffraction (NPD) and synchrotron X-ray powder diffraction (SXRPD) data in the monoclinic C2/c (No. 15) space group. This double perovskite contains a completely ordered array of alternating TmO6 and SbO6 octahedra sharing corners, tilted in antiphase along the three pseudocubic axes, with an a(-)b(-)b(-) tilting scheme, which is very unusual in the crystallochemistry of perovskites. The lead atoms occupy a highly asymmetric void with 8-fold coordination due to the stereoactivity of the Pb2+ lone electron pair. This compound presents three successive phase transitions in a narrow temperature range (at T1 = 385 K, T2 = 444 K, and T3 = 460 K in the heating run) as shown by differential scanning calorimetry (DSC) data. The crystal structure and temperature-dependent NPD follow the space-group sequence C2/c -> P2(1)/n -> R (3) over bar -> Fm (3) over barm. This is a novel polymorph succession in the high-temperature evolution of perovskite-type oxides. The Tm/Sb long-range ordering is preserved across the consecutive phase transitions. Dielectric permittivity measurements indicate the presence of a paraelectric/antiferroelectric transition (associated with the last structural transition), as suggested by the negative Curie temperature obtained from the Curie-Weiss fit of the reciprocal permittivity.