To obtain an accurate prediction model of surface roughness on the premise of low experimental cost in precision machining processes, this paper proposes two error correction models of the subsection theoretical model of arithmetic mean height roughness (Ra) in turning. The prediction performance of the two error correction models was evaluated by 25 groups of turning data of AISI1045 steel. The determination coefficient (R2) of the 10 random runs of the two correction models are both above 0.9, the mean squared error (MSE) is lower than 0.05, and the standard deviations (StdDev) of R2 and MSE are 0.01. The experimental results show that the two error correction models significantly improve the prediction accuracy and stability of the subsection theoretical model. Moreover, the influence of turning parameters and tool geometry on Ra based on the two correction models and the subsection theoretical model as well as the advantages and disadvantages of the three models is analysed, which provide an effective guidance for the selection of parameters and the prediction model in actual machining.