A major challenge in lab-on-a-chip devices is how to concentrate sample molecules from a dilute solution, which is critical to the effectiveness and the detection limit of on-chip bio-chemical reactions A numerical study of sample concentration control by electrokinetic microfluidic means in a closed-end microchannel is presented in this paper. The present method provides a simple and efficient way of concentration control by using electrokinetic trapping of a charged species of interest, controlling liquid flow and separating different sample molecules in the microchannel. The electrokinetic-concentration process and the controlled transport of the sample molecules are numerically studied in this system, in addition to the electroosmotic flow and the electrophoresis, the closed-end of the chamber causes velocity variation at both ends of the channel and induces. a pressure gradient and the associated fluid movement in the channel. The combined effects determine the final concentration field of the sample molecules The influences of a number of parameters such as the channel dimensions, electrode size and the applied electric field are investigated