IV-VI semiconductor SnSe has been known as the material with record high thermoelectric performance. The multiple close-to-degenerate (or "convergent") valence bands in the electronic band structure has been one of the key factors contributing to the high power factor and thus figure-of-merit in the SnSe single crystal. Up to date, there has been only theoretical calculations but no experimental observation of this particular electronic band structure. In this paper, using Angle-Resolved Photoemission Spectroscopy, we performed a systematic investigation on the electronic structure of SnSe.We directly observe three predicted hole bands with small energy differences between their band tops and relatively small in-plane effective masses, in good agreement with the ab-initio calculations and critical for the enhancement of the Seebeck coefficient while keeping high electrical conductivity. Our results reveal the complete band structure of SnSe for the first time, and help to provide a deeper understanding of the electronic origin of the excellent thermoelectric performances in SnSe.Thermoelectric materials could directly convert heat (many times wasted) to electrical power and therefore are of critical importance in energy industry [1][2][3][4][5][6][7]. The conversion efficiency of thermoelectric materials is quantified by the dimensionless figure of merit, = 2 ⁄ ( : Seebeck coefficient, : electrical conductivity, : total thermal conductivity, including contributions from both electrons and phonons, : temperature). Recently, singlecrystalline SnSe, a binary IV-VI semiconductor compound containing non-toxic and earthabundant elements, shows a record high ZT of ~2.6 at 923 K (along the b axis of the roomtemperature orthorhombic unit cell) [8] and the device figure of merit ~1.34 from 300-773 K when hole-doped [9], much higher than that of typical high-performance thermoelectric materials [10-15]. These excellent thermoelectric performances can be attributed to both the relatively low thermal conductivity (~0.7 Wm -1 K -1 at 300 K for the pristine samples) [8] as well as the very high Seebeck coefficient (~160 μVK -1 at 300 K with carrier density of ∼4×10 19 cm -3 ) and power factor ( 2 , ~40 μWcm -1 K -2 at 300K) [9].While the low thermal conductivity is attributed to the giant anharmonic and anisotropic bondings [8,16,17], the high Seebeck coefficient and power factor are deeply rooted in the electronic band structure of SnSe. It has been proposed that SnSe bears an electronic structure with relatively small effective mass (thus high mobility) [8,18,19] and multiple close-to-degenerate ("convergent") valence bands [9,20,21]. As the temperature increases, the carriers are thermally distributed over several convergent bands of similar energy, resulting in the enhanced Seebeck coefficient [22,23]. Besides, the most outstanding electrical conductivity and power factor along the b axis among three axes of SnSe are thought to benefit from particular "pudding-mold-like" band [24][25][26][27][28]. However, although many the...