  In this paper, we consider a coupling mechanism between the kinetic term and
the gravity, in which a coupling function $F(R)$ is introduced into the kinetic
term of the five-dimensional scalar field. Based on this scenario, we
investigate the localization of scalar fields in three specific braneworld
models: the Minkowski brane, the de Sitter brane, and the Anti-de Sitter brane.
The brane models considered here are regular with no singularity for scalar
curvature. For the Minkowshi brane case, the zero mode can always be localized
on the brane, and the massive modes can be localized or quasi-localized on the
brane. For the dS$_4$ brane case, two forms of factor $F(R)$ is considered. The
zero mode can always be localized, and the massive modes could be
quasi-localized on the brane. Besides, with the second coupling factor, the
scalar zero mode could be localized on the both sides of the origin of extra
dimension, while the massive modes could be quasi-localized on the origin.
Lastly, for the AdS$_4$ brane case, the localization of the scalar zero mode
requires the consideration of a coupling potential $V(\Phi,\varphi)$, while the
massive modes can still be localized on the brane with an infinite number.
