Wire Electrical Discharge Machining (WEDM) is widely used for machining conductive materials of intricate, complex and challenging shapes in the field of aerospace, die and mould making, automobile industries and the medical field. Proper selection of the WEDM process parameters can give good responses. Out of the various process responses, to achieve the minimum surface roughness is very difficult, due to arcing by the electrical discharge. The present investigation has been made to optimize the process parameters of WEDM during machining the Al 7075 aluminium alloy with zinc-coated copper wire using the Response Surface Methodology (RSM). Four input process parameters of WEDM, i.e., Pulse On Time, Pulse Off Time, Wire Feed and Wire Tension, were chosen as the process variables to study the process performance and to obtain the minimum surface roughness. An analysis of variance (ANOVA) was carried out to study the effect of the process parameters on the surface roughness and a mathematical model was developed. The model has been verified and checked for adequacy. The best fit surface roughness (Ra) value predicted is 1.048 μm for a Pulse On (TON) value of 120 μsec, a Pulse Off (TOFF) value of 58 μsec, a Wire Feed (WF) of 3 m/min and a Wire Tension (WT) value of 9 gm. Furthermore, it is observed that with an increase in the pulse-on time the Surface Roughness also increases, and an increase in the pulse-off time and the wire tension, the Surface Roughness decreases. Wire Feed does not influence much on the Surface Roughness.