The electron emission properties of lanthanum hexaboride (LaB6) have received much attention because its low work function, low volatility, high brightness, thermal stability and high mechanical strength. However, single crystal LaB6 is an ideal thermionic emission and field emission cathode material, its different crystal surfaces exhibit different emission properties. So far the physical factors of the emission properties of different crystal surfaces of LaB6 single crystal have been rarely reported. In this paper, the density function theory based first-principles calculations are used to analyze the electron density differences, band structures and densities of states of the typical LaB6 (100), (110), (111), (210), (211) and (310) surfaces, and the thermionic emission properties of the high-quality single crystal LaB6 typical surfaces are tested. The theoretical calculation results show that single crystal LaB6 has metal properties, electron emission characteristics and anisotropy of emission performance which are mainly caused by different crystal structures and electronic structures of LaB6 typical surfaces. The densities of La atoms in different surfaces of LaB6 single crystal are different, and a high density of La atoms in a surface is beneficial to its emission performance. The difference between relative positions for the Fermi level of different surfaces has different effect on their emission performance, and a surface with high position of Fermi level against the bottom of conduction band could have small work function and good emission performance. In addition, a surface structure of single crystal LaB6 has a large density of states and a high number of distributions of conduction band near the Fermi level, which are in favor of its electron emission. The (100) surface of single crystal LaB6 with the highest density of La atoms and electronic structure in favor of electron emission could have optimal electron emission performance compared with the remaining crystal surfaces. Thermionic emission test results show that maximum emission current densities of the (100), (110), (111), (210), (211) and (310) surfaces are 42.4, 36.4, 18.4, 32.5, 30.5 and 32.2 A/cm2 at the cathode temperature 1773 K and the voltage 1 kV. The (100) surface of LaB6 single crystal has a maximum emission current density under the same test condition, meaning that this surface has a smallest work function and best emission property compared with the other crystal surface. The thermionic emission test results show that the actual performances are basically accordant with the calculated results, demonstrating that the first principle calculation could provide a good theoretical guidance for studying the electron emission properties of rare earth hexaborides (REB6) and other cathode materials.