The spin polarization of EuB6 has been measured by using Andreev reflection spectroscopy. Analyses of the conductance spectra of the EuB6/Pb junctions yield a spin polarization of about 56%. The results demonstrate that the ferromagnetic EuB6 is not half-metallic. Combined with the Hall effect and magnetoresistivity data, the results indicate a semimetallic band structure with a fully spin-polarized hole band and an unpolarized electron band. The values and the spread of the measured spin polarization are quantitatively consistent with the experimentally determined Fermi surface and carrier densities.