A single phase $Mg_3Sb_2$ alloy was synthesized by melting the mixture of Mg and Sb metal powders at 1173 K. The figure of merit of the $Mg_3Sb_2$ prepared by melting method increased with temperature and showed a value of $2.39{ imes}10^{-2}$ at 593 K. When the $Mg_3Sb_2$ powders were milled at high speed in a planetary ball mill for 12~48 h, Zintle phase ($Mg_3Sb_2$) was maintained as a main phase, but its crystallinity became deteriorated and elemental Sb phase appeared. Sb phase free $Mg_3Sb_2$ could be obtained by the mechanical alloying of high speed ball milling for 24 h using elemental Mg and Sb powder mixtures.