Wire electrical discharge machining (WEDM) technology is a special electrothermal processing method that can precisely production of parts with variable stiffness with sharp edges or production of complex geometric parts which are difficult to produce by traditional manufacturing methods. It has an important place in production sector in terms of low energy consumption. In this study, the relationship between processing parameters on surface quality on the ferritic ductile cast iron (GGG-40) material in WEDM process with molybdenum wire was investigated by Response Surface Methodology (RSM). The aim of this study is to determine the optimum process parameters for low-cost production of GGG-40 material with sharp-edged and complex geometry parts using the WEDM method. In experimental works, surface roughness, and process time were investigated using table feedrate, pulse on time, and pulse space as cutting parameters. The surfaces obtained as a result of the experiments were evaluated in terms of surface quality with Scanning Electron Microscopy (SEM), and surface roughness device. According to the findings, it has been observed that the surface roughness has increased with increasing table feedrate, and pulse on time, and surface roughness decreased with pulse space increasing. Also, it is understood that pulse on time is the most important factor effecting surface quality. It has be en found that the process time depends on only the table federate where they are inversely proportional. As result of RSM analysis, optimum cutting parameters were obtained in terms of lowest surface roughness, lowest process time and best time/performance condition on both parameters for ferritic ductile cast iron in WEDM process.