This paper aims to discuss the periodical flow of power-law fluids with electroviscous effects through a rectangular microchannel. The complete Poisson-Boltzmann equation describing the electric potential distribution is numerically solved to be substituted into the modified Cauchy momentum equation governing the periodical pressure-driven electrokinetic flow of power-law fluids. On the basis of fourth-order compact difference methods, an effective numerical algorithm is proposed, and for Newtonian fluid the numerical solutions are compared with the analytical solutions. The time evolution of velocity field is computed for different types of fluids, periodical Reynolds numbers, zeta potentials and dimensionless electrokinetic width. The shear thinning fluids are much sensitive to the hindrance resulting from the periodical driving force, and electroviscous effects than that of Newtonian and shear thickening fluids. The hindrance reduces the velocity significantly and weakens electroviscous effects which are ignorable in the case of shear thickening fluids. Moreover, the phase offset of periodical electrokinetic flow is found for various types of fluids. (C) 2013 Elsevier B.V. All rights reserved.