In this article, the authors have attempted to use altogether a new hybrid machining process for making the holes in nickel-based superalloy (nimonic alloy) aerospace material and termed it as electro-discharge diamond drilling process. To perform this experimental study, they self-designed and developed a setup which is capable to hold as well as rotate the metal-bonded diamond abrasive tool electrode. They installed this setup on a ZNC 320 sinking electrical discharge machining machine and conducted the experimental study. The effects of input parameters such as gap current, pulse-on time, duty factor and tool rotation on the response parameters such as average surface roughness (R_a ) and average circularity (C_a ) of the drilled hole have been studied. It is observed that electro-discharge diamond drilling process has substantive effects on the improvement of R_a as well as on C_a in comparison to the hole made by stationary electrode electrical discharge machining (die-sinking electrical discharge machining) process. The photographs and micrographs of few selected workpieces were taken by metallurgical microscope and scanning electron microscope, respectively, which commensurate with the findings of the research study.