Understanding electroosmotic now of non-Newtonian fluid in microchannels is of both fundamental and practical significance for optimal design and operation of various microfluidic devices. A numerical Study of electroosmotic flow in microchannels considering the non-Newtonian behavior has been carried out for the first time. One lattice Boltzmann equation is solved to obtain the electric potential distribution in the electrolyte, and another lattice Boltzmann equation which avoids the derivations of the velocity data to calculate the shear is applied to obtain the flow field for commonly used power-law non-Newtonian model. The simulation results show that the fluid rheological behavior is capable of changing the electroosmotic flow pattern significantly and the power-law exponent n plays an important role. For the shear thinning fluid of n < 1, the electrical double layer effect is confined to a smaller zone close to the wall surface and it is more inclined to develop into a plug-like flow whilst the shear thickening fluid of n > 1 is more difficult to grow into the plug-like flow compared to Newtonian fluid. (C) 2008 Elsevier B.V. All rights reserved.