The work aims to establish a grey correlation degree prediction model of surface roughness and residual stress and determine the optimization scheme of micro-milling process parameters, to minimize residual stress on the basis of reducing surface roughness. Firstly, a three-factor three-level micro-milling test was designed by BBD test method, and the surface roughness and residual stress of workpiece were measured. Secondly, taking the signal-to-noise ratio of surface roughness and residual stress as performance indexes, multiple targets were converted into a single target for optimization based on grey correlation analysis. Thirdly, on the basis of principal component analysis, a second-order regression prediction model between grey correlation analysis (GRA) and process parameters was established. Finally, the response surface method (RSM) was used to obtain the optimal combination of parameters. The average error of grey correlation degree prediction model was 6.9% and the optimized results were improved by 3.91%. According to the experimental results, the optimal processing parameters were as follows: the spindle speed of 20 000 r/min, the axial cutting depth of 60 μm, and the feed speed of 285.8 mm/min. Therefore, the grey correlation degree prediction model has good fitting degree and high reliability and accuracy, and the combination of process parameters based on the method proposed in this paper can achieve the optimal solution of surface roughness and residual compressive stress at the same time.