This paper presents a mathematical model to describe a two-fluid electroosmotic pumping technique, in which an electrically non-conducting fluid is delivered by the interfacial viscous force of a conducting fluid; the latter is driven by electroosmosis. The electrical potential in the conducting fluid and the analytical solution of the steady two-fluid electroosmotic stratified flow in a rectangular microchannel was presented by assuming a planar interface between the two immiscible fluids. The effects of viscosity ratio, hold-up, concentration, and interfacial zeta potential are analyzed to show the potential feasibility of this technique.