  In this paper we investigate the localization and mass spectra of bulk matter
fields on a Gergory-Rubakov-Sibiryakov-inspired braneworld. In this braneworld
model, there are one thick brane located at the origin of the extra dimension
and two thin branes at two sides. For spin 1/2 fermions coupled with the
background scalar $\phi$ via $\eta\bar{\Psi}\phi^p\Psi$ with $p$ a positive odd
integer, the zero mode of left-hand fermions can be localized on the thick
brane for finite distance of the two thin branes, and there exist some massive
bound modes and resonance modes. The resonances correspond to the
quasi-localized massive fermions. For free massless spin 0 scalars, the zero
mode can not be localized on the thick brane when the two thin branes are
located finitely. While for a massive scalar $\Phi$ coupled with itself and the
background scalar field $\phi$, in order to get a localized zero mode on the
thick brane, a fine-tuning relation should be introduced. Some massive bound
modes and resonances also will appear. For spin 1 vectors, there is no bound KK
mode because the effective potential felt by vectors vanishes outside the two
thin branes. We also investigate the physics when the distance of the two thin
branes tends to infinity.
