A modified multi-component solute diffusion equation described with diffusion flux was derived in detail based on the classical Maxwell-Stefan diffusion theory. The friction between the solute species and the soil skeleton wall, which is proportional to the relative velocity between the solute species and the soil skeleton, is introduced. The chemical potential gradient is considered the driving force. A one-dimensional model for transport of multi-component solute in saturated soil was developed based on the modified diffusion equation and the modified competitive Langmuir adsorption equation. Numerical calculation of a case of two heavy metal ion species, which was chosen as an example, was carried out using the finite element software COMSOL Multiphysics. A comparative analysis was performed between the multi-component solute transport model developed in this study and the convection-diffusion transport model of single-component solute based on Fick’s law. Simulation results show that the transport behavior of each species in a multi-component solute system is different from that in a single-component system, and the friction characteristics considered in the developed model contribute to obstructing the movement of each solute component. At the same time, the influence of modified competitive Langmuir adsorption on solute transport was investigated. These research results can provide strong theoretical support for the design of antifouling barriers in landfills and the maintenance of operation stability.