In order to obtain the accurate prediction model of surface roughness in precision machining processes, this paper researches the subsection theoretical model for surface roughness in turning built by our research group, which considers feed rate, nose radius and tool minor cutting edge angle, and proposes two error correction models of the subsection theoretical model for improving theoretical model accuracy. The prediction performance of two error correction models is evaluated by 25 groups of turning data. The experimental results show that two error correction models have excellent prediction performance and significantly improve the prediction accuracy and stability of the subsection theoretical model. Moreover, the influence of turning parameters and tool geometry on surface roughness based on the three models, and the advantages and disadvantages of three models in prediction performance and test cost are analyzed, which provide an effective guidance for selection of parameters and the prediction model of surface roughness in the actual turning.