The electronic structure of ultrathin Bi(001) films on Si(111)-7×7 was studied by spin and angle-resolved photoemission spectroscopy. We directly observed a clear momentum-dependent spin splitting and polarization of the surface-state bands. The spin structure was antisymmetric with respect to the Γ̅ point as predicted by theory, and the obtained in-plane spin polarization was as high as ±0.5. The qualitative features of the observed spin polarization are discussed in comparison with the spin-polarized band structure obtained by first-principles calculations.