The present study has numerically investigated two-dimensional electro osmotic flows in channel equipped with two symmetric periodic arrays of square-sectioned ribs with one-fifth of the channel half-width in size. For the simulation, the ionic-species and electric-potential equations as well. as the continuity and momentum ones are solved using the finite volume method. Instead of assuming the Boltzmann distribution, the Nernst-Plank equation is applied for the ionic species. Results show that the steady electro osmotic flow and ionic distributions depend strongly on the EDL length and streamwise periodic length. For a sufficiently large periodic length, the fluid flows along the wall as in the inviscid flow at a small EDL length compared with the rib size, whereas it flows with involving two recirculation bubbles around the rib as in the pressure-driven flow at a large EDL length. At an intermediate EDL length comparable to the rib size, a very intricate flow pattern is observed around the rib. With decreasing periodic length, on the other hand, the interaction between two adjacent ribs gets stronger and thus the flow pattern significantly changes. This study would contribute to further understanding electroosmotic flows in micro- and nanofluidic devices of complicated geometries.