We report on p-type conductivity in antimony (Sb)-doped ZnO (ZnO:Sb) nanorods which have self-corrugated surfaces. The p-ZnO:Sb/n-ZnO nanorod diode shows good rectification characteristics, confirming that a p-n homojunction is formed in the ZnO nanorod diode. The low-temperature photoluminescence (PL) spectra of the ZnO:Sb nanorods reveal that the p-type conductivity in p-ZnO:Sb is related to the Sb(Zn)-2V(Zn) complex acceptors. Transmission electron microscopy (TEM) analysis of the ZnO:Sb nanorods also shows that the p-type conductivity is attributed to the Sb(Zn)-2V(Zn) complex acceptors which can be easily formed near the self-corrugated surface regions of ZnO:Sb nanorods. These results suggest that the Sb(Zn)-2V(Zn) complex acceptors are mainly responsible for the p-type conductivity in ZnO:Sb nanorods which have corrugated surfaces.