In electrical discharge machining (EDM), different area of the tool electrode had different wear rate when it prepared by the different materials. Based on this characteristic, this paper used Sn-coated Cu foils to fabricated the CuSn functional gradient electrode (CuSn-FG electrode). Through electroplating technology, we electroplated Sn foil on both sides of the Cu foil and the Sn-coated Cu foils were obtained. By placing the Sn-coated Cu foils in the vacuum furnace for heat treatment, the Sn element diffused into the interior of the Cu foil and the CuSn-FG electrodes were fabricated. Using tungsten cobalt cemented carbide (YG8) as workpiece, the CuSn-FG electrodes were applied in EDM to machine micro-groove. The Sn element cannot be uniformly distributed inside the CuSn-FG electrode, causing different resistivity in different regions of the CuSn-FG electrode. Consequently, the different regions in CuSn-FG electrode had different EDM wear, which can be used to machine micro-groove. In this study, the effect of heat treatment parameters on the fabrication of CuSn-FG electrode and its EDM performance were investigated. Based on the above research, a mathematical model between the cross-sectional profile of micro-groove and CuSn-FG electrode was established based on the BiDoseResp model. This mathematical mode was used to predict the cross-sectional profiles of the micro-grooves fabricated by EDM of CuSn-FG electrodes heat-treated at different temperatures. Analyzing the prediction results and the experimental results, we found that the relative error of the mathematical model was less than 5 %, indicating the accuracy of the mathematical model.