A transport model that considers convection, diffusion, and finite kinetic rate on the membrane column as well as the influence of extra column dispersion and lag times, was used in this study to mathematically describe the frontal adsorption behaviour of plasmid DNA in an ion-exchange membrane chromatography system. The corresponding partial differential equations system was solved using the numerical method of lines (MOL) on a MATLAB platform. Experimental data from literature describing the frontal adsorption of pCI DNA in an ion-exchange membrane column was used as a model system for validation of MOL solution of the transport model. This approach results in a unique way to predict frontal performance and it is a valuable tool to assess the use of membrane adsorbers in large scale processes for plasmid purification.