Surface roughness is an important parameter to evaluate the quality of a machining process in mechanical manufacturing. The construction of a surface roughness model of a machining process is the basis for predicting surface roughness corresponding to each certain case. This paper presents the construction of a surface roughness model in 080A67 steel turning. An experimental process was carried out with a total of 15 experiments, designed according to the Box-Behnken matrix. The cutting speed, feed rate, and cutting depth were changed in each experiment, and surface roughness values were measured to build a model that showed the mathematical relationship between surface roughness and the three cutting parameters. A second surface roughness model was also constructed using the Box-Cox transformation. The accuracy of these two models was compared through five coefficients: R2, R2(pred), R2(adj), Percentage Absolute Error (PAE), and Percentage Square Error (PSE). The results showed that all these coefficients of the model using the Box-Cox transformation were better than those of the first one. In detail, the values of R2, R2(pred), R2(Adj), PAE, and PSE of the first model were 94.55%, 12.79%, 84.74%, 8.79%, and 1.42%, while for the second model were 99.09%, 85.42%, 97.44%, 2.26%, and 0.18%, respectively, showing that the accuracy of the surface roughness model was improved by using the Box-Cox transformation.