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α-MgAgSb is considered as a potential near-room-temperature thermoelectric material in virtue of its excellent electrical properties, ultralow lattice thermal conductivity and abundant constituent elements. However, it is hard to obtain high-quality phase pure α-MgAgSb due to its complex phase transition and high reactivity of element Mg, which cloaks material's intrinsic thermoelectric performance. Herein, through adopting a tantalum-sealing melting technique, we achieved highly-quality pure α-MgAgSb with large grain size and less oxygen content, as compared with our ball milled samples. The as-synthesized tantalum-sealing melted α-MgAgSb, without element doping or alloying, exhibited intrinsically low thermal conductivity, large weighted mobility, and high carrier concentration closes to the optimum range. Eventually, we attained a maximum thermoelectric figure of merit zT value of 1.3 at around 500 K in the tantalum-sealing melted α-MgAgSb. The average power factors and average zT values are also as high as 25 μW cm−1 K−2 and 1.1 respectively in the low-temperature range of (300 - 550) K, both of which rank as top values among the known materials. This study not only sheds new light on the understanding of intrinsic properties of α-MgAgSb but also demonstrates its great promise for harvesting low-grade waste heat. Record-high average power factor of 25 μW cm−1 K−2 and average zT of 1.1 were achieved in the melted α-MgAgSb sythesized by the tantalum-sealing melting technique. [Display omitted] [ABSTRACT FROM AUTHOR]