Undoped and slightly Eu-doped SmB₆ samples show the opening of a gap with decreasing temperature below  ∼ 150 K. The spectral shapes near the Fermi level (E_F) at 15 K have shown a marked increase in intensity of the peak at a binding energy (E_B) of approximately 12 meV with decreasing photon energy (hν) from 17 to 7 eV. Angle-resolved spectra of SmB6 measured at hν = 35 eV just after the in situ cleavage showed clear dispersions of several bands in the E_B region from E_F to 4 eV. Spin-polarized photoelectron spectra were then measured at 12 K and a light incidence angle of  ∼ 50^°. In contrast to the lack of spin polarization for the linearly polarized light excitation, clear spin polarization was observed in the case of circularly polarized light excitation. The two prominent peaks at E_B  ∼  12 and  ∼ 150 meV have shown opposite signs of spin polarization which are reversed when the helicity of the light is reversed. The sign and magnitude of spin polarization are consistent with a theoretical prediction for the ⁶H_5/2 and ⁶H_7/2 states.