Drilling of Carbon Fiber-Reinforced Plastic/Titanium alloy (CFRP/Ti) stacks represents one of the most widely used machining methods for making holes to fasten assemblies in civil aircraft. However, poor machinability of CFRP/Ti stacks in combination with the inhomogeneous behavior of CFRP and Ti alloy face manufacturing and scientific community with a problem of defining significant factors and conditions for ensuring hole quality in the CFRP/Ti alloy stacks. Herein, we investigate the effects of drilling parameters on drilling temperature and hole quality in CFRP/Ti alloy stacks by applying an artificial neuron network (ANN). We varied cutting speed, feed rate, and time delay factors according to the factorial design L9 Taguchi orthogonal array and measured the drilling temperature, hole diameter, and out of roundness by using a thermocouple and coordinate measuring machine methods for ANN analysis. The results show that the drilling temperature was sensitive to the effect of stack material layer, cutting speed, and time delay factors. The hole diameter was mainly affected by feed, stack material layer, and time delay, while out of roundness was influenced by the time delay, stack material layer, and cutting speed. Overall, ANN can be used for the identification of the drilling parameters–hole quality relationship.