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Electrophoresis-polishing method, it is one of the methods of "Field-assisted Fine Finishing (FFF)", has been developed recently, in which charged grains suspended in liquid move to an electorode under an applied potential. Present paper focuses on effect of electrophoresis current yielded by the movement of the charged grains in liquid under the applied potential. Effect of grain concentration of CeO 2 and ZrO 2 fine abrasives on the electrophoresis-polishing both of BK7 glass and silicon wafer is examined experimentally. It is found that -potential of CeO 2 and ZrO 2 fine abrasives dispersed into liquid are measured by moving boundary method on simple setup using the electrophoresis phenomenon of the charged grains, on which the electrical double layer is conducted. The result of examinations presents controllability by the applied potential and independence for grain concentration. Polishing setup is able to give the polishing pressure to the work piece on the unwoven polisher made of polymer. Experimental results show that the stock removal increases with increasing the applied potential. Concerning the increase of stock removal in the conditions of high concentration of grain, influence of the electrophoresis current is discussed relating with the flow of polishing compound.