The uniaxial tensions of single crystal Cu nanowires (NWs) with different circular cross-section radiuses are simulated by molecular dynamics (MD) method. Atomic interactions in Cu NWs are described by EAM potential. The results show that the plastic deformation of NWs under uniaxial tension is dominantly controlled by dislocation nucleation and gliding. The mechanical properties of NWs are size-dependent. The NWs with larger radius of cross-section possess higher strength and ductility. Furthermore, the site of neck formation and following break of NWs has strong dependence on size scale of NWs.