In this work optimization of turning parameters for turning Ti-6Al-7Nb Titanium alloy has been investigated by orthogonal array along with Grey relational analysis coupled with principle component. Parameters such as surface roughness, tool wear, roundness, material removal rate, temperature and power consumption are considered as performance characteristics of the turning process. By orthogonal array eighteen experiments are carried out in the CNC machine by considering cutting environment, cutting speed, feed rate, depth of cut, nose radius, tool coating type and insert shape angle as turning parameters. From the grey relational grade the optimum turning parameters were predicted. Also the influence of individual turning parameters is carried out by Analysis of Variance. From the largest value of grey relational grade parameters , cutting environment: wet, feed rate : 0.08 mm /rev, cutting speed: 100 m/min ,insert angle: 80 0 , nose radius: 0.4 mm, tool coating type : TiAlN and depth of cut:0.4 mm are found to be better turning parameters levels. About 11.3 % enhancement of grey relation grade value is achieved when compared to initial parameter grey relational grade value.