In the present work few process parameters of a Jig Boring machine like 'Feed Rate', 'Depth of Cut' and 'Cutting Speed' have been optimized for best possible values of few performance parameters or target parameters like 'Vertical Reaction Force', 'Surface Roughness' and 'Material Removal Rate' for a Mild Steel work specimen. The grade of the steel used in the specimen is AISI 1040. Though optimization of process parameters of a Jig Boring machine has been done by many researchers or engineers previously, in the present work a mathematical model has been formulated by regression analysis from the experimental data created as per Taguchi method. Next, from the experimental data, Grey Relational Analysis has been done to predict the optimum combination of process parameters for the best result of performance parameters. Lastly, to validate the mathematical model which has been derived by regression analysis, optimization of the process parameters have been done using Genetic Algorithm optimization tool of MATLAB Program and the optimum result of the process parameters have been verified with the optimum result determined by Grey Relational Analysis.