The chemical stability of ZnO against acidic dye molecules is an important issue to be improved in a dye-sensitized solar cell (DSSC). In this study, ZnO nanowires (ZnO-NWs) are prepared on a FTO glass through chemical bath deposition, and then the surface of ZnO-NWs are precisely coated with a thin TiO2 layer step by step using a simple dipping–rinse–hydrolyzation (DRH) process to create the core–shell structure of ZnO@TiO2 nanowires (ZnO@TiO2-NWs) for improving the chemical stability of ZnO. This core–shell structure of ZnO@TiO2-NWs on a FTO glass is further used as the photoanode of a DSSC with an acidic N3 dye as sensitizer. The TiO2 shell acts not only as a protective layer to avoid the formation of Zn2+/dye complexes on the surface of ZnO-NWs, but also as a barrier against the recombination of injected electrons with the triiodide ions at the interface of ZnO-NWs and the electrolyte. A higher efficiency of 1.17% is achieved for the core–shell ZnO@TiO2-NWs based DSSC with optimized dye sensitization time and DRH cycles, when compared to the optimized cell with pristine ZnO-NWs (0.75%).