Wheel and rail wear is a significant issue in railway systems. Accurate prediction of this wear can improve economy, ride comfort, prevention of derailment and planning of maintenance interventions. Poor prediction can result in failure and consequent delay and increased costs if it is not controlled in an effective way. However, prediction of wheel and rail wear is still a great challenge for railway engineers and operators. The aim of this paper is to predict wheel wear and rail wear using an artificial neural network. Nonlinear Autoregressive models with exogenous input neural network (NARXNN) have been developed for wheel and rail wear prediction. Testing with a twin disc rig, together with measurement of wear using replica material and a profilometer have been carried out for wheel and rail wear under dry, wet and lubricated conditions and after sanding. Tests results from the twin disc rig have been used to train, validate, and test the neural network. Wheel and rail profiles plus load, speed, yaw angle, and first and second derivative of the wheel and rail profiles were used as an inputs to the neural network, while the output of neural network was the wheel wear and rail wear. Accuracy of wheel and rail wear prediction using the neural network was investigated and assessed in term of mean absolute percentage error (MAPE). The results demonstrate that the neural network can be used efficiently to predict wheel and rail wear. The methods of collecting wear data using the replica material and the profilometer have also proved effective for wheel and rail wear measurements for training and validating the neural network. The laboratory tests have aimed to validate the wear predictions for realistic wheel and rail profiles and materials but they necessarily cover only a limited set of conditions. The next steps for this work will be to test the methods for rail and wheel data from field tests.