A numerical investigation of an electroosmotic flow through a microchannel is presented. Lattice Poisson-Boltzmann method was utilized to determine the effective geometrical and electrokinetic parameters in a microfluidic system. The non-Newtonian fluid model is assumed to be viscoplastic which is suitable for modeling biologic structures. These types of fluids are shown to have a yield stress which affects the velocity profile significantly. Unlike Casson fluid constitutive properties, electrokinetic parameters are shown not to be effective on the yielded region in the microchannel. The influence of flow and viscokinetic parameters on yield height, plug-flow velocity and mass flow rate was studied and discussed.