  In this paper, we investigate the localization and the mass spectra of
gravity and various bulk matter fields on a thick anti-de Sitter (AdS) brane,
by presenting the mass-independent potentials of the Kaluza-Klein (KK) modes in
the corresponding Schr\"{o}dinger equations. For gravity, the potential of the
KK modes tends to infinity at the boundaries of the extra dimension, which
leads to an infinite number of the bound KK modes. Although the gravity zero
mode cannot be localized on the AdS brane, the massive modes are trapped on the
brane. The scalar perturbations of the thick AdS brane have been analyzed, and
the brane is stable under the scalar perturbations. For spin-0 scalar fields
and spin-1 vector fields, the potentials of the KK modes also tend to infinity
at the boundaries of the extra dimension, and the characteristic of the
localization is the same as the case of gravity. For spin-1/2 fermions, by
introducing the usual Yukawa coupling $\eta\bar{\Psi}\phi\Psi$ with the
positive coupling constant $\eta$, the four-dimensional massless left-chiral
fermion and massive Dirac fermions are obtained on the AdS thick brane.
