The composites are currently gaining significant place among various materials due to their unique features. The Technological advancement in the materials sector has created curiosity among the research community to create new materials with different and required properties. Among the newly developed materials, Carbon Fibre Reinforced Carbon composite material is occupying very important place. This composite is also known as carbon-carbon composite material and used mostly in the fabrication of advanced structures like rockets, space shuttles, missiles, aircrafts etc. Generally CFRC composites are very expensive and the drilling cost addition of these materials makes them much more expensive. Hence the machining parameters are carefully selected, so that no drilling damage is caused during machining. The main objective of this paper is to determine the optimal drilling parameters by using a unique multi response optimization technique known as GRA. The drilling experiments were carried out on a CFRC composite plate with a 10mm Solid Carbide tool on the VMC100 CNC drilling machine, at Anna University, Chennai campus, India. The experiments were planned as per Taguchi’s L₂₇ orthogonal array. Drill bit point Angle, Spindle speed and Feed rate were chosen as the process control factors. The drilling performance is evaluated by Thrust Force, Torque and Surface Roughness.