In this study, the effects of cutting parameters on the surface roughness in Wire Electrical Discharge Machining (WEDM) of Waspaloy have been investigated and optimal cutting parameters for lowest surface roughness values were determined. As control factors; wire tension, wire feed speed, feed rate and dielectric flushing pressure have been selected and a Taguchi L18 (2(1)x3(3)) orthogonal array was used for experimentation. The statistical effects of cutting parameters on the surface roughness have been determined by using analysis of variance (ANOVA). The second order predictive equation has been developed via Linear Regression Analysis. Using the second-order predictive surface roughness equation developed in the result of this study, the theoretical average surface roughness (R-a) values at a confidence level of 95 percent (R-2=0.936) have been obtained. When evaluating the main effects plots and ANOVA results, the feed rate was found the most efficient factor on the Ra, while dielectric flushing pressure and wire speed were the following ranking factors. The wire tension was seemed to have not of a statistically influence on the R-a. The arithmetic average surface roughness R-a of the WEDM-cut workpiece has been obtained between 2.683 to 4.052 mu m intervals for Waspaloy.