Experimental data on the thermoelectric properties of p-type CoSb3 reported by Caillat et al. [J. Appl. Phys. 80, 4442 (1996)] have been analyzed, assuming not only a pair of the first valence (v1) and the first conduction (c1) bands but also the second valence (v2) and the second conduction (c2) bands. By taking into account the excitation of carriers into the v2 and the c2 bands, the behavior of the Hall coefficient as well as that of the Seebeck coefficient at high temperatures is well explained. By taking into account the nonparabolicity of the v1 band, the temperature dependence of mobility is well explained with assuming scattering due to acoustic phonons, nonpolar and polar optical phonons, and ionized impurities. Furthermore, various material parameters of CoSb3, such as the band-gap energy, effective masses, and deformation potentials, have been deduced from fitting the calculation to the experimental data on the temperature dependences of the Hall coefficient, the mobility, and the Seebeck coefficient. Among them, the band-gap energy and the effective mass of the v1 band have been corrected from the original values estimated by Caillat et al. In addition, it is shown that the experimental data on the hole-concentration dependences of both the room-temperature Seebeck coefficient and the cyclotron mass are well reproduced by the theoretical calculation using the deduced values for the nonparabolic v1 band.