Making real-life decisions regarding selection of optimum parameters in machining of materials, especially when faced with conflicting objectives, is a tough task. Multi-objective methods are usually used to deal with such problems. This article applies grey relational analysis to the multi-responses that were obtained during turning of AISI 304 austenitic stainless steels on a computer numerical control lathe. The experiments were conducted using the Taguchi design of experiments technique. In grey relational theory, a grey relational grade is found such that it indicates an optimum level of machining parameters that produce smaller magnitudes of surface roughness, flank wear, tool vibrations and a higher magnitude of material removal rate. The combination of the following machining parameters produces a better turning performance: speed of 210 m/min, feed rate of 0.15 mm/rev, depth of cut of 1.0 mm and a nose radius of 0.4 mm. The significant factors affecting the overall responses of turning process were evaluated by analysis of variance. Thereafter, optimum values of overall responses were predicted. Finally, a second-order multi-objective model was developed, which relates the machining parameters to the grey relational grade using response surface methodology.