We report high-precision Mg isotopic analyses of different types of lunar samples including two pristine Mg-suite rocks (72415 and 76535), basalts, anorthosites, breccias, mineral separates, and lunar meteorites. The Mg isotopic composition of the dunite 72415 (δ25Mg = −0.140 ± 0.010‰, δ26Mg = −0.291 ± 0.018‰), the most Mg-rich and possibly the oldest lunar sample, may provide the best estimate of the Mg isotopic composition of the bulk silicate Moon (BSM). This δ26Mg value of the Moon is similar to those of the Earth and chondrites and reflects both the relative homogeneity of Mg isotopes in the solar system and the lack of Mg isotope fractionation by the Moon-forming giant impact. In contrast to the behavior of Mg isotopes in terrestrial basalts and mantle rocks, Mg isotopic data on lunar samples show isotopic variations among the basalts and pristine anorthositic rocks reflecting isotopic fractionation during the early lunar magma ocean (LMO) differentiation. Calculated evolutions of δ26Mg values during the LMO differentiation are consistent with the observed δ26Mg variations in lunar samples, implying that Mg isotope variations in lunar basalts are consistent with their origin by remelting of distinct LMO cumulates.