The electronic structure of thin Co nanoislands on Cu(111) has been investigated below and above the Fermi level (EF) by scanning tunneling spectroscopy at low temperature. Two surface related electronic states are found: a strong localized peak 0.31 eV below EF and a mainly unoccupied dispersive state, giving rise to quantum interference patterns of standing electron waves on the Co surface. Ab initio calculations reveal that the electronic states are spin polarized, originating from d_3z²−r²-minority and sp-majority bands, respectively.