Machining of hard metal is difficult by conventional method to obtain high accuracy where the dimensional accuracy is the main factor. Wire electrical discharge machining (WEDM) extensively used, which is mostly used in machining of conductive materials by using precisely controlled sparks that occur between a very thin wire and a workpiece in the presence of a dielectric fluid. This study serves in studying surface roughness (SR) of high speed steel (HSS) using taguchi method to design the experiment, this was achieved with utilizing different wire cut machining parameters and study the behavior of these control parameters such as pulse duration (μs), pulse interval (μs), Servo feed and Servo voltage (V) on surface roughness. It can be noticed that when servo voltage and servo feed increase the surface roughness decreases and when pulse duration and pulse interval increase the surface roughness increases too, and It was found with using taguchi parameter design that the best machining variables of combination setting is Servo Voltage (22) volts, Pulse on time (110) μs, servo feed (450) mm/min and Pulse off time (30) μs to reach to the minimum value of surface roughness and hence better surface finish.