Concern about the transport of chemicals in groundwater systems has stimulated the development of many models to describe transport in porous media, the most common of which under steady-state conditions is the convection–dispersion equation (CDE). We propose a novel solution to the CDE for predicting profiles of solute concentrations and estimating transport parameters. The solution was adapted from polynomial and exponential boundary-layer (BL) solutions based on BL theory. The accuracy of the new BL solution was dependent on the number of polynomial terms and the properties of the soil. The errors in predicting profiles of solute concentrations and estimating transport parameters were usually lower for a model combining one exponential and two polynomial terms than for a model with only one polynomial term. The new BL solution provides an alternative for simulating solute transport under field conditions and improves the methodology of using BL theory to solve the CDE.