  It has been found that the zero mode of a five-dimensional Elko spinor could
be localized on branes by introducing a Yukawa-type coupling between the Elko
spinor and the background scalar field or the Ricci scalar. However, the
Yukawa-type coupling is not appropriate for all brane models. In this paper, we
explore other localization mechanism for the Elko spinor by introducing the
non-minimal coupling $f(\phi)\mathfrak{L}_{Elko}$ between the five-dimensional
Elko spinor and the background scalar field. We give the general expressions of
the Elko zero mode and the function $f(\phi)$. Through two thick brane models
and three concrete examples, we show that the Elko zero mode can be localized
on the branes by this new mechanism. This provides us more possibilities of
localizing the Elko zero mode.
