In order to improve the quality and productivity the present study highlights the optimization of CNC end milling process parameters to provide good surface finish. The surface finish has been identified as one of the main quality attribute and is directly related to the productivity of a machine. In this paper an attempt has been made to optimize theprocess such that the best surface roughness value can be obtained in a process. Hence a multi objective optimization problem has been obtained which can be solved by the hybrid Taguchi method comprising of principal components analysis as well as utility theory. To meet the basic assumption of taguchi method in the present work individual response correlation has been eliminated first by means of Principal components analysis (PCA). Correlated responses have been transformed into uncorrelated quality indices called as principal components. From the principal components the quality loss estimates have been calculated and the Grey relational values are found out for the quality loss estimates. Then the overall grey relational grade has been calculated. Finally taguchi method has been used to solve the optimization problem. Simultaneous optimization of huge number of responses can be done using the aforesaid method.