In this article, electroosmotic flow of non-Newtonian fluids through a curved rectangular microchannel is studied numerically. The power-law model is used to simulate the rheological behavior of fluid. Moreover, the flow is assumed to be hydrodynamically fully developed and the walls carry high zeta potentials. To do so, the Poisson-Boltzmann equation without imposing the Debye-Huckel linear approximation is solved by applying the central difference scheme. Furthermore, the continuity and Cauchy momentum equations in the cylindrical coordinate system are solved using SIMPLE finite-volume method. Consequently, the effects of governing parameters such as flow behavior index, electrokinetic separation distance, curvature, zeta potential, and channel aspect ratio on the flow field and hydrodynamic characteristics are studied in details. The results show that the secondary flows which are created in shear-thinning fluid flows are stronger in comparison to that of shear-thickening and Newtonian fluid flows. Also, the variation of electrokinetic separation distance changes the secondary flow patterns in shear-thinning fluid flows, and it does not have a monotonic effect on the strength of secondary flows. Moreover, the obtained results for shear-thinning and Newtonian fluid flows indicate that the increasing of curvature, in addition to increasing the circulation strength considerably, also causes the volumetric flow rate to slightly increase. Furthermore, it is found that the increasing of zeta potential can be employed in shear-thinning fluid flows in order to significantly increase the volumetric flow rate and the performance of mixing. Additionally, it is observed that the increasing of channel aspect ratio leads to an increase in the circulation strength of shear-thinning fluid flow.