The present study highlights a multi-objective optimization problem by applying Weighted Principal Component Analysis (WPCA) coupled with Taguchi method through a case study in cylindrical grinding of UNS C34000 Medium Leaded Brass. The study aimed at evaluating the best process environment which could simultaneously satisfy multiple requirements of surface quality. In view of the fact that traditional Taguchi method fails to solve a multi-objective optimization problem, to overcome this limitation, WPCA has been coupled with Taguchi method. Furthermore, to follow the basic assumption of Taguchi method, i.e., quality attributes should be uncorrelated or independent; which is not always satisfied in practical situation; the study applied WPCA to eliminate response correlation and to evaluate independent or uncorrelated quality indices called principal components which were aggregated by WPCA to compute overall quality index denoted as Multi-Response Performance Index. A combined quality loss was then estimated which was optimized (minimized) finally. The study combined WPCA and Taguchi method for predicting optimal setting. Optimal result was verified through confirmatory test. This indicates application feasibility of the aforesaid methodology proposed for multi-response optimization and off-line control of correlated multiple surface quality characteristics in cylindrical grinding.