Skutterudite CoSb_3 crystals attract much attention as one of candidates for thermoelectric material with a high value in thermoelectric figure-of-merit. Electronic structures of skutterudite CoSb_3 were calculated with a discrete variational (DV)-Xα method. The calculated total density of states (DOS) is in agreement with the experimental results obtained by means of ultraviolet photoemission (UPS) and inverse-photoemission (IPES) spectra. The calculated Co 3d partial DOS (PDOS) distribute over 0 to 6 eV in the valence band. This is in agreement with the results obtained from Co 3p-3d resonant photoemission measurements (RPES). It is found that contribution from the hybridization between Co 3d and Sb 5p states to the valence band is important in skutterudite CoSb_3.