In laser microdrilling, the formation of taper and the dimension of the heat-affected zone (HAZ) are important attributes that greatly influence the quality of a drilled hole. In this article, an experimental investigation into Nd:YAG laser microdrilling of alumina is carried out to produce desired high-quality microdrill. Four independently controllable process variables viz. lamp current, pulse frequency, air pressure, and pulse width are considered as input parameters, while hole taper and HAZ width are considered the output parameters. The Taguchi method combined with the grey relational analysis is used as a statistical design of experiment technique to set the optimal process parameters. The objective is set to minimize both quality characteristics, simultaneously. Grey relational analysis is applied to convert the multiple quality characteristics to a single performance characteristic, called grey relational grade. Optimal process parameters are then determined by the Taguchi method using grey relational grade as the quality index. Both of the quality characteristics of drilled holes are improved markedly at the optimal process condition, as verified by an additional confirmation test. This indicates the application feasibility of the grey-based Taguchi technique for continuous improvement of laser microdrilling quality in the manufacturing industry.