Introducing boundary-layer (BL) theory to solve problems of solute transport provides a simple and accurate alternative method to estimate transport parameters. Most BL solutions to the convection–dispersion equation (CDE) are derived from the hypothesis of a zero concentration gradient at the position of solute front, which is inconsistent with the actual situation. This study assumes a logarithmic concentration profile and presents a novel analytical solution to the equilibrium CDE. The concentration gradient at solute front for the logarithmic model is not regarded as zero. A range of parameter values was used to evaluate the accuracy of the logarithmic model based on the relative error between the logarithmic and the corresponding exact profiles, and soil-column experiments were used to examine the reliability of the model for parameter estimation. The accuracy of the new BL solution was greatly influenced by the values of the transport parameters. The logarithmic profile matched the exact profile well when the rate of change of concentration was large in shallow porous media. These findings will integrate the methodology of using BL theory to solve problems of solute transport and provide a more accurate method for some cases of solute transport.