This article presents an approach which first combines grey relational grade and weighted quality loss function to convert the values of multiple responses obtained from each of the Taguchi orthogonal designed experiments into a single performance evaluation value. Then the analysis of variance (ANOVA) and the SN ratio based Taguchi analysis are conducted to find out respectively the relative importance of the process parameters and a set of near optimal parameter settings. A validation experiment is then conducted to confirm the finding. A case of multi-response turning process optimization is used to illustrate the proposed approach. Two sets of weights for the total quality loss were applied and the results were compared. The effectiveness of this approach was demonstrated by the improvement of turning performance in the both weight settings.