A mathematical model based on the lubrication theory is presented for quasi-one-dimensional electroosmotic flow of a power-law fluid through a slit microchannel with undulating and non-uniformly charged walls. The channel height and the wall potential may vary periodically with axial position, with a wavelength much longer than the average channel height. Owing to the nonlinear rheology, the pressure gradient that is internally induced to satisfy continuity of flow has to be found numerically. A trial-and-error method is adopted to search for a flow rate that will give rise to an axial pressure gradient distribution with a zero average over one wavelength of the channel. When the flow behavior index is equal to the reciprocal of an integer, polynomial equations relating the flow rate and the local pressure gradient can be deduced, which will greatly facilitate the seeking of the solution by trial and error. Numerical results are also presented to illustrate how the flow behavior index may qualitatively change the combined effect of the geometric and electrokinetic wall patterns on the flow rate.