Ti-6Al-4V Extra Low Interstitial (ELI) exhibits superior properties because of controlled interstitial element of iron and oxygen. The effects of four cutting parameters namely cutting speed, feed, depth of cut and tool nose radius on responses like cutting force, average cutting temperature and surface roughness have been investigated for turning of Ti-6Al-4V (ELI). Total 81 experiments have been performed in dry environment. Grey Relational Analysis has been used for multi-objective optimization. Analysis of Variance test has been carried out to investigate contribution of input parameters. The model was found fit with R-Square value of 88.74%. Regression and ANN models are developed for prediction and compared. From the Grey relational analysis, it is clear that optimum parameters to minimize cutting force, cutting temperature and surface roughness while turning Ti-6Al-4V (ELI), are cutting speed as 140 rpm, Nose radius 1.2mm, Feed 0.051mm/rev and depth of cut is 0.5mm. In comparison of regression model, the ANN model is found to be more accurate with average error of 3.57%.