  Localization of a spin-$1/2$ fermion on the braneworld is an important and
interesting problem. It is well known that a five-dimensional free massless
fermion $\Psi$ minimally coupled to gravity cannot be localized on the
Randall-Sundrum braneworld. In order to trap such a fermion, the coupling
between the fermion and bulk scalar fields should be introduced. In this paper,
localization and quasilocalization of a bulk fermion on the thick braneworld
generated by two scalar fields (a kink scalar $\phi$ and a dilaton scalar
$\pi$) are investigated. Two types of couplings between the fermion and two
scalars are considered. One coupling is the usual Yukawa coupling
$-\eta\bar{\Psi}\phi\Psi$ between the fermion and kink scalar, another one is
$\lambda\bar{\Psi}\Gamma^{M}\partial_{M}\pi\gamma^{5}\Psi$ between the fermion
and dilaton scalar. The left-chiral fermion zero mode can be localized on the
brane, and both the left- and right-chiral fermion massive Kaluza-Klein modes
may be localized or quasilocalized. Hence the four-dimensional massless
left-chiral fermion and massive Dirac fermions, whose lifetime is infinite or
finite, can be obtained on the brane.
