Advanced engineering materials (e.g., nickel or titanium alloy) are being increasingly applied to produce parts of gas turbines in the aerospace industry. To improve the durability of these parts, many holes, with a length-to-diameter aspect ratio greater than 20:1, are created in their structure. The quality of the holes significantly affects the cooling process of the elements. However, it is challenging to machine materials by conventional methods. When machining a hole with a high aspect ratio, the major problem is effective flushing of the machining area, which can improve the hole’s surface integrity and dimensional accuracy. Consequently, the electro-discharge drilling (EDD) process is good alternative for this application. This paper presents the results of an analysis of the EDD of Inconel 718 alloy. An experiment was conducted to evaluate the impact of process parameters (pulse time, current amplitude, and discharge voltage) on the process’s performance (linear tool wear, taper angle, drilling speed, the hole’s aspect ratio, and surface roughness ( Ra and Rz )). The results show that EDD provides us with the possibility to drill holes with an aspect ratio greater than 10:1. The results also demonstrate that holes with an aspect ratio greater than 10:1 and a small taper angle value have a significantly decreased quality of internal surface, especially at the bottom of the hole. This indicates that an insufficient amount of debris is removed from the bottom of the hole.