Most of the bio-fluids are non-Newtonian fluid with complex flow behavior, for instances the human blood and DNA sample are shear thinning fluids. The transportation of such fluids shares wide applications in microfluidics. The mathematical model for the two immiscible layers electro-osmotic driven flow in the parallel microchannel is proposed in this paper. One layer is conducting non-Newtonian power-law fluid driven by electro-osmotic force. The other layer is non-conducting Newtonian layer driven by interface shear. The effects of Debye-Huckel parameter kappa h(1), interfacial zeta potential psi(1), the Newtonian viscosity mu(2), the non-Newtonian fluid consistency coefficient m & flow behavior index n are discussed. The complex flow behavior, namely fluid consistent coefficient and flow behavior index, play important roles upon the velocity distributions. The shear thinning effect is also analyzed. The results show that the shear thinning fluid is not only ideal for direct electro-osmotic driving but also for hybrid driving. (C) 2014 Elsevier Ltd. All rights reserved.