The time-dependent aspects of pressure-driven three-liquid flow under the effect of electroosmotic flow (EOF) are analytically studied, in which non-conducting liquid is delivered by the pressure gradient and the interfacial viscous forces of two conducting liquids, the two conducting liquids are driven by electroosmosis and pressure gradient. The flow of the three liquids depends on the coupling effects between them, which involve the electrokinetic effect. The surface charges at the liquid-liquid interface are accounted in this model. At the interface, the shear stress is not continuous because of the presence of the surface charges. With Laplace transform method, an analytical solution of such time-dependent three-liquid flow in rectangular channel is presented.