  An asymmetric thick domain wall solution with de Sitter ($dS$) expansion in
five dimensions can be constructed from a symmetric one by using a same scalar
(kink) with different potentials. In this paper, by presenting the
mass-independent potentials of Kaluza--Klein (KK) modes in the corresponding
Schr\"{o}dinger equations, we investigate the localization and mass spectra of
various bulk matter fields on the symmetric and asymmetric $dS$ thick branes.
It is shown that the spectrum of scalar KK modes on the symmetric $dS$ brane
contains only one bound mode (the massless mode). However, for the asymmetric
$dS$ brane with a large asymmetric factor $a$, there are two bound scalar KK
modes: a zero mode and a massive mode. For spin 1 vectors, the spectra of KK
modes on both $dS$ branes consist of a bound massless mode and a set of
continuous ones, i.e., the asymmetric factor does not change the number of the
bound vector KK modes. For spin 1/2 fermions with the scalar-fermion coupling
$\eta\bar\Psi \sin(\phi/\phi_0)\cos^{-\delta}(\phi/\phi_0)\Psi$, there exist
some discrete bound KK modes and a series of continuous ones. The asymmetric
factor $a$ reduces the number of the bound fermion KK modes.
