The artificial neural network method (ANN) is widely used in both modeling and optimization of manufacturing processes. Determination of optimum processing parameters plays a key role as far as both cost and time are concerned within the manufacturing sector. The burnishing process is simple, easy and cost-effective, and thus it is more common to replace other surface finishing processes in the manufacturing sector. This study investigates the effect of burnishing parameters such as the number of passes, burnishing force, burnishing speed and feed rate on the surface roughness and microhardness of an AZ91D magnesium alloy using different artificial neural network models (i.e. the function fitting neural network (FITNET), generalized regression neural network (GRNN), cascade-forward neural network (CFNN) and feed-forward neural network (FFNN). A total of 1440 different estimates were made by means of ANN methods using different parameters. The best average performance results for surface roughness and microhardness are obtained by the FITNET model (i.e. mean square error (MSE): 0.00060608, mean absolute error (MAE): 0.01556013, multiple correlation coefficient (R): 0.99944545), using the Bayesian regularization process (trainbr)). The FITNET model is followed by the FFNN (i.e. MAE: 0.01707086, MSE: 0.00072907, R: 0.99932069) and CFNN (i.e. MAE: 0.01759166, MSE: 0.00080154, R: 0.99924845) models with very small differences, respectively. The GRNN model has noted worse estimation results (i.e. MSE: 0.00198232, MAE: 0.02973829, R: 0.99900783) as compared with the other models. As a result, MSE, MAE and R values show that it is possible to predict the surface roughness and microhardness results of the burnishing process with high accuracy using ANN models.