The mechanical drilling of micro holes is considered a difficult endeavor, due to the high hardness and brittleness of alumina plates found during the drilling process. In this work, an alumina plate with a 4mm thickness is drilled with the use of a continuous-wave Nd:YAG fiber laser. As can be seen, there is minimum required power density to ablate the alumina plate. As shown in this study, the hole diameter and straightness are not constant with the hole depth recorded, which is presumably due to the recondensation of vaporized alumina, and the characteristics of irregular laser radiation. The oxygen pressure, power density, focal position, and laser on time (duration) are chosen as the control parameters. To understand the influence of control parameters, the orthogonal arrays table in Taguchi method is applied, and the micro holes are evaluated based on the use of geometrical factors. Through the review of a sensitivity and interaction analysis, the appropriate duration and oxygen pressure are identified as the major parameters governing the geometrical quality of drilled holes in this study.