Ti-6Al-4V (grade 5 titanium alloy) is one of the most widely used materials in aerospace applications including turbine blades for aerospace engines. Due to the difficulty of machining titanium alloys using conventional machining processes, wire-electro-discharge machining (wire-EDM) is used extensively for cutting titanium parts with complex geometries and profiles. The objective of this study is to investigate the effect of two important non-electrical parameters in wire-EDM, i.e. wire feed rate and wire tension, on the geometric corner and profile accuracies of the Ti-6Al-4V parts machined by wire EDM. A complex profile was designed for machining in two different thicknesses of titanium alloy using each set of experimental parameters. The complex part includes corners with 45°, 90° and 112.5°, as well as thin wall section for measuring the kerf accuracy. It was found that with the increase of wire tension, the corner accuracies at almost all the angles improved. however, too high wire tension caused inaccuracies by providing larger angles than the target values. The effect of wire tension was dependent on the thickness of the machined part. For thinner workpiece the results of the angles generated barely followed a trend, whereas for thicker part, the measured angles followed an excellent trend. The kerf accuracies were found to improve with the increase of wire tension for thin part, whereas for thick part the results of kerf width accuracies were inconsistent. In case of wire feed rate, it was found that comparatively lower settings of wire feed rates were favorable for machining thinner parts with enhanced corner accuracies. On the other hand, slightly higher wire feed rates provided better corner accuracies for thick part. Besides corner inaccuracy, profile undercuts and deviations from the machining paths were observed for lower wire tensions. Finally, it can be concluded that comparatively lower wire feed rate and higher wire tension provides improved corner and profile accuracies. however, for machining thinner sections using wire-EDM, the trends are not obvious.