The present deals with some investigations on surface roughness during hard machining of EN 24 steel with the help of coated carbide insert. The experiment has been done under dry conditions. The optimization of process parameters have been done using Grey based Taguchi approach. Also the prediction models have been developed using regression analysis for surface roughness and adequacy has been checked. Good surface quality of roughness about 0.42 microns is obtained in hard machining. Using grey-based Taguchi approach, the optimal parametric combination for surface quality characteristics (Ra and Rz) have been obtained to be depth of cut: 0.4mm, feed: 0.04mm/rev and cutting speed: 130 m/min respectively. Feed is considered to be the most dominant parameter for both surface roughness parameters Ra and Rz. The prediction models have high correlation coefficient (R2 = 0.993 and 0.934). This is evident to be better fitting of the model and found to be high significance.