A neural-network-based methodology is proposed for predicting the surface roughness in a turning process by taking the acceleration of the radial vibration of the tool holder as feedback. Upper, most likely and lower estimates of the surface roughness are predicted by this method using very few experimental data for training and testing the network. The network model is trained using the back-propagation algorithm. The learning rate, the number of neurons in the hidden layer, the error goal, as well as the training and the testing dataset size, are found automatically in an adaptive manner. Since the training and testing data are collected from experiments, a data filtration scheme is employed to remove faulty data. The validation of the methodology is carried out for dry and wet turning of steel using high speed steel and carbide tools. It is observed that the present methodology is able to make accurate prediction of surface roughness by utilising small sized training and testing datasets.