It is possible to improve the hole quality by reducing the delamination which occurs in the drilling of carbon fibre reinforced plastic (CFRP) composite plates. For this study, carried out under dry machining conditions, the parameters included three different cutting speeds, three different feed rates and drill geometry involving three different point angles. The Taguchi L9 orthogonal array experimental design was selected and the optimum cutting parameters and drill geometry for reducing the damage factor to a minimum were determined. The optimum test conditions were achieved using the parameter combination of 118° point angle, 30 m/min cutting speed and 0.06 mm/rev feed rate (A1B1C1). In addition, variance analysis (ANOVA) was conducted to determine the effect rate of the parameters on the damage factor. The variable having the greatest effect on the damage factor was found to be the point angle (47.66%), followed by the cutting speed (24.44%) and feed rate (19.82%). The conditions for minimising delamination damage in the drilling of the CFRP plates were optimised successfully by using the Taguchi test design.