This study develops a 1-D mass transport model to describe the electrophoresis transport behavior within a microchannel with a variable cross-sectional area. Utilizing three different numerical schemes, simulations are performed to investigate the IEF of proteins in ampholyte-based pH gradients within both a planar microchannel and a contraction-expansion microchannel, respectively. The simulation results obtained using the modified 1-D mass transport model and the finite-volume method (FVM) for the IEF separation of a single protein sample in a ten-ampholyte-based pH gradient within a planar microchannel are consistent with those presented by Shim et al. [Electrophoresis 2007, 28, 572-586] using a 2-D FVM scheme. In addition, the Courant-Friedrichs-Lewy number insensitive conservation element and solution element (CNI-CESE) method is found to be both more robust and more computationally efficient than the conventional CESE scheme when modeling IEF phenomena within a contraction-expansion microchannel. In modeling the IEF separation of four sample ampholytes in a 20-ampholtye-based pH gradient within a contraction-expansion microchannel, the results obtained using the CNI-CESE scheme are in good agreement with those published in literature. Moreover, the simulations can be performed significantly faster with the new 1-D model and the CNI-CESE scheme. Finally, the results obtained using the modified 1-D mass transport model and the CNI-CESE scheme demonstrate that the concentration of the focused test sample and the resolution of the pH gradient within the microchannel increase as the number of ampholytes used to accomplish the IEF separation process is increased.