To improve the surface quality of the copper and reduce the diamond tool wear, a prediction model is established experimentally for the relationship between surface roughness and machining parameters. Based on the processing principle of flycutting machining, the prediction model for surface roughness is set up by response surface methodology. Then, a machining experiment for the copper is conducted under different cutting parameters designed by Taguchi method and the surface roughness is tested by 4D technology dynamic laser interferometer. After that, the prediction model is obtained by analyzing the experimental data, and the accuracy of the model is verified by analysis of variance (ANOVA), R 2 value and residual analysis. Furthermore, the effect of cutting parameters upon the surface roughness is analyzed. Finally, validation tests are conducted to verify the model. Experimental results demonstrate that the prediction model is adequate at 95% confidence level. The output of prediction model helps to select cutting parameters to reduce surface roughness which ensures surface quality in ultra-precision fly cutting machining.