CFRP/Ti6Al4V ((Carbon fiber reinforced plastic composite/Ti6Al4V titanium alloy) stacks have been widely used in the modern aerospace industry owing to its superior mechanical/physical properties and excellent structural functions. Drilling is one of the important machining operations for assemble of CFRP/Ti6Al4V stacks. However, delamination, which is an undesirable type of damage to CFRP that seriously jeopardizes the mechanical properties of the material around the hole during drilling of the CFRP/Ti6Al4V stacks occurs and, the delamination factor is used to determine the degree of this delamination. The aim of this study is to determine the optimal levels of drilling parameters in order to minimize delamination in the hole input and exit of CFRP in the through-hole drilling of CFRP/Ti6Al4V stacks with step uncoated carbide drills. For this purpose, drilling experiments on the CFRP/Ti6Al4V stacks were carried out with reference to the Taguchi L18 orthogonal array experimental design at the different cutting speeds, feed rates and drilling strategies. The multiple performance optimization of the drilling parameters for the minimization of hole input delamination factor  (Dfg) and the hole exit delamination factor (Dfç) was performed by the Gray Relation Analysis (GIA) method. Optimal levels of drilling parameters for minimum hole input and exit delamination factor at CFRP when drilling CFRP/Ti6Al4V stacks with step uncoated carbide drills; 14 m/min cutting speed, 0.040 mm/rev feed rate and drilling strategy starting from CFRP towards Ti6Al4V. The most effective drilling parameters on the delaminations at the hole input and exit of CFRP were the drilling strategy and the feed rate, the effect of the cutting speed remained below 5%.