Bright and stable structured green luminescence (GL) is achieved from solution-grown Cu-doped ZnO nanorods. Dependence of photoluminescence on the annealing parameters reveals that GL is correlated with creation of Zn vacancies (VZn) and then formation of Cu dopants at Zn sites (CuZn). High internal quantum efficiency (43%) of the GL can be sustained up to 240 K due to negative thermal quenching. In contrast to the poor stability of defects-related visible emission, the structured GL shows good stability with respect to sample heating. Cu-doped ZnO nanorods with strong and stable GL have potential applications in visible light display and lighting.