Spin-polarized tunneling was studied on Co surfaces of exchange coupled Co/Cu/Co samples, using an Fe tip. A spin-polarized surface state of Co(0001) was found to exist at -0.43 eV relative to E(F), with FWHM of 0.23 eV in the spectra. The state exhibits negative magnetoresistance with an effective spin polarization of less than -23%, suggesting negatively high spin polarization of the surface state. Our first-principles calculations have supported the existence of the surface state. From the calculation, the state is identified as a minority spin Gamma-centered d(2)(z)-like surface state.