The structural and electronic properties of the CdS/ZnS core-shell nanowires (NWs) oriented along [001] direction have been investigated by means of the first-principles calculation. It is found that CdS core suffers from the compressive strain in the CdS-core/ZnS-shell NWs, and ZnS core is stretched in the ZnS-core/CdS-shell NWs. A thicker ZnS shell can improve the NWs' stability, and a thicker CdS shell would decrease their stability. For both CdS/ZnS core-shell NWs, the band gap decreases linearly with increasing the shell when the core size is fixed. However, when the diameter of NWs is fixed, CdS-core/ZnS-shell NWs with a thicker shell would have larger band gap. The results agree well with that of red-shift or blue-shift of the spectrum in experimental observations. The partial density of states indicates that the contribution to valence band maximum mainly comes from the S-3p state, and the contribution to conduction band minimum mainly comes from Cd-5s state for CdS-core/ZnS-shell NWs. Thus the electrons would be effectively confined in CdS core, and the holes tend to distribute over both the core and shell. It can be deduced that CdS-core/ZnS-shell NWs with a thicker shell may have larger mobility.