The simple binary compound SnSe has been reported as a robust thermoelectric material for energy conversion by showing strong anharmonicity and multiple electronic valence bands. Herein, we report a record-high average ZT value of similar to 1.6 at 300-793 K with maximum ZT values ranging from 0.8 at 300 K to 2.1 at 793 K in p-type SnSe crystals. This remarkable thermoelectric performance arises from the enhanced power factor and lowered lattice thermal conductivity through crystal structure modification via Te alloying. Our results elucidate that Te alloying increases the carrier mobility by making the bond lengths more nearly equal and sharpening the valence bands; meanwhile, the Seebeck coefficient remains large due to multiple valence bands. As a result, a record-high power factor of similar to 55 mu W cm(-1) K-2 at 300 K is achieved. Additionally, Te alloying promotes Sn atom displacements, thus leading to a lower lattice thermal conductivity. Our conclusions are well supported by electron localization function calculations, the Callaway model, and structural characterization via aberration-corrected scanning transmission electron microscopy. Our approach of modifying crystal structures could also be applied in other low-symmetry thermoelectric materials and represents a new strategy to enhance thermoelectric performance.