ZnO nanowires (NWs) with a ZnS coating are synthesized in order to modify the surface without changing the diameter of the NWs. They have the wurtzite ZnO at the core and a cubic ZnS at the outer layer. The NWs show a sharp ultraviolet and a broad visible emission of the photoluminescence spectra. Surface modification has led to a change in the position of the maxima of the visible emission in ZnO-ZnS NWs. The photocarrier relaxation under steady UV illumination occurs in ZnO NW arrays but is absent in ZnO-ZnS NW arrays. The dark current value for both type of NWs are similar, whereas the photocurrent value is much higher in the surface-modified NWs. Higher photocurrent value indicates a transport of the photogenerated carriers from the ZnS layer to ZnO during UV illumination. The carrier transport mechanism is proposed through a model.