Residual nuclide production is studied experimentally by bombarding a Cu target with a 250 MeV proton beam. The data are measured by the off-line gamma-spectroscopy method. Six nuclides are identified and their cross sections are determined. The corresponding calculated results by the MCNPX and GEANT4 codes are compared with the experimental data to check the validity of the codes. A comparison shows that the MCNPX simulation has a better agreement with the experiment. The energy dependence of residual nuclide production is studied with the aid of MCNPX simulation, and it is found that the mass yields for the nuclides in the light mass region increase significantly with the proton energy.