This paper presents the numerical results of fluid flow and mixing in a microfluidic device for electro-osmotic flow (EOF) with an trapezoidal electrode array on the bottom wall (ETZEA). Differently from previous EOF in a channel which only transports fluid in colloidal system. ETZEA can also be utilized to mix a target liquid with a reagent. In this study we propose a method of controlling fluid flow and mixing enhancement. To obtain the flow and mixing characteristics, numerical computations are performed by using a commercial code, CFX-10, and a self-made code LBM-D. It was found that the flow near the trapezoidal electrode in the ETZEA is of 3-D complex flows due to the zeta potential difference between the trapezoidal electrode and channel walls, and as a consequence the hetrogeneous zeta potential on the electrodes plays an important role in mixing the liquid.