We report results of a self-consistent full-potential linearized augmented-plane-wave calculation within the local-density approximation for an 11-layer slab corresponding to a Cu(110) surface. The relaxed geometry, i.e., the change of the top two interlayer spacings ${\mathrm{\ensuremath{\Delta}}}_{12}$=-6.2% and ${\mathrm{\ensuremath{\Delta}}}_{23}$=+2.1% was obtained by total-energy minimization. For the work function, a value of 4.84 eV was derived. Based on the self-consistent potentials of the electronic-structure calculation for the relaxed geometry, angle-resolved inverse-photoemission spectra were calculated within a one-step model. Spectra were obtained for the \ensuremath{\Gamma}\ifmmode\bar\else\textasciimacron\fi{}-X\ifmmode\bar\else\textasciimacron\fi{} and \ensuremath{\Gamma}\ifmmode\bar\else\textasciimacron\fi{}-Y\ifmmode\bar\else\textasciimacron\fi{} symmetry lines. Two surface-related states at X\ifmmode\bar\else\textasciimacron\fi{} and Y\ifmmode\bar\else\textasciimacron\fi{} were found at 4.6 and 1.5 eV above the Fermi energy.