Understanding solute transport process is of fundamental significance for industrial and natural processes such as mixing and separation. Since detailed information for the transverse concentration distribution is required for associated applications, compared with the sole consideration of the cross-sectional mean concentration in previous studies, the present paper analytically explores the complete spatial concentration distribution in packed tube flow by the proposed two-scale perturbation analysis (Z. Wu, G.Q. Chen, Journal of Fluid Mechanics, 740 (2014) 196-213.). With modification on the zeroth-order concentration up to the first-order, the deduced analytical solution gives a good prediction for the longitudinal distribution of mean concentration as well as the transverse distribution, according to comparisons with new results of numerical simulation. Importantly we show in the paper that instead of being uniformly distributed in the cross-section as expected in traditional view, the transverse concentration is highly non-uniform when Taylor dispersion model is applicable. Representing the complicated flow conditions for packed tube flow, the unique dimensionless parameter as a damping factor affects the complete spatial concentration distribution in two ways: cause the contraction of the solute concentration cloud, and the flattening of the concentration contours. (C) 2015 Elsevier Ltd. All rights reserved.