Owing to the special structure of a five-dimensional Elko spinor,its localization on a brane with codi-mension one becomes completely different from that of a Dirac spinor.By introducing the coupling between the Elko spinor and the scalar field that can generate the brane,we have two types of localization mechanism for the five-dimensional Elko spinor zero mode on a brane.One is the Yukawa-type coupling,and the other is the non-min-imal coupling.In this study,we investigate the localization of the Elko zero mode on de Sitter and Anti-de Sitter thick branes with the two localization mechanisms,respectively.The results show that both the mechanisms can achieve localization.The forms of the scalar coupling function in both localization mechanisms have similar proper-ties,and they play a similar role in localization.