Wire-electrical-discharge machining (WEDM) is a modification of electro-discharge machining (EDM) and has been widely used for a long time for cutting punches and dies, shaped pockets and other machine parts on conductive materials. WEDM erodes workpiece materials by a series of discrete electrical sparks between the workpiece and an electrode flushed or immersed in a dielectric fluid. The WEDM process is particularly suitable for machining hard materials as well as complex shapes. In this paper, a neural network and the Taguchi design method have been implemented for minimizing the surface roughness in a WEDM process. A back-propagation neural network (BPNN) was developed to predict the surface roughness. In the development of a predictive model, machining parameters of open-circuit voltage, pulse duration, wire speed and dielectric flushing pressure were considered as the input model variables of the AISI 4340 steel. An analysis of variance (ANOVA) was used to determine the significant parameter affecting the surface roughness (R-a). Finally, the Taguchi approach was applied to determine the optimum levels of machining parameters.