A three-parameter (positive odd integers, thickness factor, and asymmetry factora) family of asymmetric thick brane solutions in five dimensions were constructed from a two-parameter (s and) family of symmetric ones in [R. Guerrero, R.O. Rodriguez, and R. Torrealba, Phys. Rev. D72, 124012 (2005).]. The values s = 1 and s 3 correspond to single branes and double branes,respectively. These branes have very rich inner structure. In this paper, by presenting the massindependent potentials of Kaluza–Klein (KK) modes in the corresponding Schrodinger equations,we investigate the localization and mass spectra of fermions on the symmetric and asymmetric thick branes in an AdS background. In order to analyze the effect of gravity-fermion interaction (i.e., the effect of the inner structure of the branes) and scalar-fermion interaction to the spectrum of fermion KK modes, we consider three kinds of typical kink-fermion couplings. The spectra of left chiral fermions for these couplings are consisted of a bound zero mode and a series of gapless continuous massive KK modes, some discrete bound KK modes including zero mode (exist mass gaps) and a series of continuous massive KK modes, infinite discrete bound KK modes, respectively. The structures of the spectra are investigated in detail.