A hitherto unknown sodium magnesium plumbide, Na2MgPb, was synthesized by heating the constituent elements. Na2MgPb crystallizes in a hexagonal unit cell with the Li2CuAs-type structure (P6(3)/mmc, Z = 2, a = 5.110(2) angstrom, c = 10.171(4) angstrom at 293 K). The compound furthermore displays polymorphism: high-temperature powder XRD measurements revealed that hexagonal Na2MgPb (dubbed the "alpha" phase) transforms to another hexagonal phase (beta) which is existent at 493-553 K, and the beta phase changes to a cubic structure (gamma) at 533-633 K further. The molar volume of gamma-Na2MgPb is approximately 9% and 13% smaller than the molar volumes of the a phase and the beta phase, respectively (at 543 K). The electrical resistivity of Na2MgPb is 0.39 m Omega at 300 K; it rises with increasing temperature from 300 to 491 K, and then drops at 491 and 523 K. These abrupt changes in resistivity may be attributed to the alpha -> beta and beta -> gamma phase transitions, respectively. To gain further insight into the structure of cubic gamma-Na2MgPb, putative models with regular Heusler-type (Cu2MnAl-type) and inverse Heusler-type (Li2AgSb-type) arrangements were probed using first-principles computations based on density functional theory (DFT). These computations indicate that, for the cubic gamma phase, an inverse Heusler-type structure is distinctly more stable than the alternative regular Heusler type (at 0 K); beyond that, ab initio thermochemistry was successfully used to verify the stability ordering (alpha-Na2MgPb being favorable at low temperature, gamma-Na2MgPb at high temperature), albeit the theoretically predicted transition temperature of 900 K which is higher than observed in experiment.