ZnO:Cu/ZnO core/shell nanocrystals are synthesized by a two-step solution-phase process. The morphology, structure and optical properties of the samples are detected by scanning electron microscopy, Raman, absorption and luminescence spectroscopy. The increase of particle size confirms the growth of ZnO shell. The segregation of CuO phase observed in ZnO: Cu core is not detected in ZnO:Cu/ZnO core/shell nanocrystals from Raman spectra. It is suggested that some Cu ions can be segregated from ZnO nanocrystals, and the separated Cu ions can be incorporated inside ZnO shell after the growth of ZnO shell. The visible emission mechanism is discussed in detail, and the photoluminescence analysis indicates that the core/shell structure helps to eliminate the surface-related emission.