In the present research, laser micro-drilling of alumina has been investigated experimentally. The laser used is Nd:YAG, having a wavelength of 1.06 μm. The process parameters investigated are: lamp current, pulse frequency, air pressure and pulse width. The quality of micro-holes is evaluated by measuring the hole taper and HAZ width. Response surface methodology is adopted to perform the experimental design and also to develop the mathematical relationships relating the input process parameters and output qualities. The adequacy of the models is tested by statistical measures. Finally, the developed mathematical models are used for sensitivity analysis to identify the critical parameters and their tendencies.