The unsteady electroosmotic flow characters of power-law fluids in a finite micro-diffuser are studied in this paper. Based on the Ostwald-de Wael model which is used to describe power-law fluids (the shear thinning, thickening and Newtonian fluids), high accuracy compact difference schemes are used to solve the two-dimensional Poisson-Nernst-Planck equations and the modified Cauchy momentum equations. Electroosmotic flow distributions of power-law fluids at initial instant and steady state are numerically simulated in this paper. It is presented that while the radius of the diffuser is increasing, the dimensionless apparent viscosity influenced by shear strain conduces to the different velocity profiles of power-law fluids. In the micro-diffuser, the shear strains of pseudo plastic and dilatant fluids are decreasing with the radius increasing and the apparent viscosity of pseudo plastic fluid is increasing with the shear strain decreasing, but the apparent viscosity of dilatant fluid is decreasing with the shear strain decreasing. The apparent viscosity of power-law fluids can estimate the flow performance, and the fluid with high viscosity flows more slowly than the one with low viscosity. The numerical results show that a fast speed response of power-law fluid is found near the wall at the beginning and the average dimensionless velocity of power-law fluids is decreasing with the radius increasing when fixing the diffuser angle and dimensionless electrokinetic diameter at the same dimensionless zeta potentials. At the initial instant, the different velocity distributions of power-law fluids from upstream to downstream near the wall in diffuser are essentially due to the change of dimensionless shear strain. Because the dimensionless shear strains of pseudo plastic and dilatant fluids are in a larger value zone in upstream, the dimensionless apparent viscosity of dilatant fluid is larger than that of the pseudo plastic fluid, and the velocity peak of pseudo plastic fluid is larger than that of the dilatant fluid. In downstream, the apparent viscosity of pseudo plastic fluid is larger than that of the dilatant fluid so that their velocity peaks are similar. At the steady state, the velocity profiles of power-law fluids are plug-like and the velocity is decreasing with increasing radius when the continuity conditions are satisfied, and the flow regularity of Newtonian is just like that on a macroscopic scale. The velocity profile of pseudo plastic fluid is larger than that of dilatant fluid in upstream and their velocity profiles in downstream are not much different. The power-law fluid flow distribution at initial instant is similar to that at the steady state. From the flow regularities respectively at initial instant and the steady state it follows that the flow rate of pseudo plastic fluid is larger than that of Newtonian fluid and the dilatant fluid flow rate is smaller than Newtonian fluid rate. At the initial instant, under the same electrokinetic diameter and different zeta potentials, the difference in shear strain among power-law fluids in the micro-diffuser near the wall leads to the difference in the apparent viscosity, and eventually leads to the velocity distribution difference between pseudo plastic and dilatant fluids.