This work presents an analytical attempt to illustrate the effect of axial diffusion on concentration dispersion in packed tube flows. The concentration moment method is applied to derive the analytical solution for time-dependent Taylor dispersion coefficient. With the increase in the packing parameter alpha as a damping factor, the concentration dispersion is characterized by three modes: (I) the shear-induced dispersion dominated mode, with dispersion coefficient determined by alpha; (II) the transition mode; and (III) the diffusion dominated mode, with dispersion coefficient determined by Peclet number Pe. In contrast to the usually negligible effects of axial diffusion for dispersion in pure fluid flows even at a relatively small Pe, axial diffusion with typical cc plays an important role for packed media flows even with large Pe. (C) 2015 Elsevier Ltd. All rights reserved.