Electro discharge machining (EDM) is one of the most frequently used processing methods for machining conductive materials. Taguchi method combined with Grey relational method has been used to accommodate requests for multiple object functions in the EDM process. In the present study, an attempt was made to determine optimum parameters for minimum size of hole and number of shots. The size of the hole is related to the quality of the hole while the number of shots affects machining time. Grey relational analysis was used to determine optimal machining parameters. Electrode length and unit discharge were found to be the most significant parameters. Optimal conditions were: pulley position of 39 ㎜, voltage of 120 V, a capacitance of 1500 pF, and a resistance of 500 Ω. In experiments, such electrical conditions (voltage, capacitance, and resistance) generated electrical energy of 10 μj. Under these conditions, a micro hole of 184.9 ㎛ in average diameter could be machined with 16 shots.