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This paper discusses the application of the Taguchi method to optimize the machining parameters for machining of GFRP composite in drilling for individual responses such as thrust force and delamination factor. Moreover, a multi-response performance characteristic is used for optimization of process parameters with application of grey relational analysis. An orthogonal array (L9), grey relational generation, grey relational coefficient and grey – fuzzy grade obtained from the grey relational analysis applied as performance index to solve the optimization problem of drilling parameters for GFRP composite. Taguchi orthogonal array, the signal-to-noise ratio, and the analysis of variance are used to investigate the optimal levels of cutting parameters. The confirmation tests are conducted to verify the results and it is observed that grey-fuzzy approach is efficient in determining the optimal cutting parameters.