Thermoelectric technology, harvesting electric power directly from heat, is a promising environmentally friendly means of energy savings and power generation. The thermoelectric efficiency is determined by the device dimensionless figure of merit ZT(dev), and optimizing this efficiency requires maximizing ZT values over a broad temperature range. Here, we report a record high ZT(dev) similar to 1.34, with ZT ranging from 0.7 to 2.0 at 300 to 773 kelvin, realized in hole-doped tin selenide (SnSe) crystals. The exceptional performance arises from the ultrahigh power factor, which comes from a high electrical conductivity and a strongly enhanced Seebeck coefficient enabled by the contribution of multiple electronic valence bands present in SnSe. SnSe is a robust thermoelectric candidate for energy conversion applications in the low and moderate temperature range.