Composite structures gain significant attention in the last decade due to their high specific strength and modulus when compared to their metallic counterparts. Although molding technique is used to produce near net shape composite structures, post processing (e.g., drilling) is still required to meet the dimensional tolerances and enable assembly. Drilling of composite structures is a complex process and needs special care to ensure the desired hole quality. The holes on the composite plates must be free of drilling-induced delamination and micro-crack to provide good strength and fatigue in the assemblies. In this study, effect of the cutting parameters on the quality of holes drilled in a Glass Fiber Reinforced Thermoset Polymer was investigated with the delamination factor defined as the ratio of intended hole diameter to the diameter of the maximum area which contains both hole and delaminated area. For this purpose, Taguchi`s L9 orthogonal array was used to design the experiments and optimize the drilling parameters. 5 mm twist drill bits were used to drill the holes at the feeds of 400 mm/min, 600 mm/min, and 800 mm/min, and spindle speeds of 4000 rpm, 6000 rpm, and 8000 rpm. The maximum diameters on the inlet and outlet sides of the holes drilled into the composite plates were then measured with an optical microscope to analyze the influence of the drilling parameters on the machining damage. The obtained results indicate that the quality of a hole drilled on a glass fiber reinforced thermoplastic polymer can be improved by setting the optimized process parameters.