Inconel 625 is one of the most versatile nickel-based super alloy used in the aerospace, automobile, chemical processing, oil refining, marine, waste treatment, pulp and paper, and power industries. Wire electrical discharge machining (WEDM) is the process considered in the present text for machining of Inconel 625 as it can provide an effective solution for machining ultra-hard, high-strength and temperature-resistant materials and alloys, overcoming the constraints of the conventional processes. The present work is mainly focused on the analysis and optimization of the WEDM process parameters of Inconel 625. The four machining parameters, that is, pulse on time, pulse off time, spark gap voltage and wire feed have been varied to investigate their effects onthree output responses, such as cutting speed, gap current, and surface roughness. Response surface methodology was used to develop the experimental models. The parametric analysis-based results revealed that pulse on time and pulse off time were significant, spark gap voltage is the least significant, and wire feed as a single factor is insignificant. Multi-objective optimization technique was employed using desirability approach to obtain theoptimal parameters setting. Furthermore, surface topography in terms of machining parameters revealed that pulse on time and pulse off time significantly deteriorate the surface of the machined samples, which produce thedeeper, wider overlapping craters and globules of debris.