Glass Fiber Reinforced Plastics composites have an increased application in recent days, due to its enhanced structural properties, Mechanical and thermal properties. Drilling of holes in GFRP becomes almost unavoidable in fabrication. The heterogeneous nature of this kind of materials makes complications during machining operation. However, drilling is a common machining practice for assembly of components. The quality of holes produced in the GFRP material is severely affected by surface roughness, Circularity and Delamination. The objective of the study is to apply the Taguchi method and ANOVA to achieve an improved hole quality considering the minimum surface roughness through proper selection of drilling parameters. The regression method is employed in the Experimental investigation and Mathematical modelling of drilling of GFRP material using HSS drill bits.